a) Find a recurrence relation that would determine the number of sequences a1, a2, ., an that have an odd number of zeros when each a, E { 0, 1, 2}, in terms of the number of sequences of n-1 of these elements that do. For example when n=3 we would have the sequences 000, 001, 002, 010, 011, 012, 020, 021, 022, 100, 101, 102, 110, 111, 112, 120, 121, 122, 200, 201, 202, 210, 211, 212, 220, 221, 222. These sequences consist of all of the base 3 numbers that can be made using 3 digits. = 12 If we let T(n) = # of these sequences with an odd number of 0's, we would get for n=3 that T(3) b) Determine the base condition for this recurrence relation and determine by iteration a closed form formula for the value of the recurrence relation for any number of digits n. C) Prove that your formula is correct.

a) Find a recurrence relation that would determine the number of sequences a1, a2, ., an that have an odd number of zeros when each a, E { 0, 1, 2}, in terms of the number of sequences of n-1 of these elements that do. For example when n=3 we would have the sequences 000, 001, 002, 010, 011, 012, 020, 021, 022, 100, 101, 102, 110, 111, 112, 120, 121, 122, 200, 201, 202, 210, 211, 212, 220, 221, 222. These sequences consist of all of the base 3 numbers that can be made using 3 digits. = 12 If we let T(n) = # of these sequences with an odd number of 0's, we would get for n=3 that T(3) b) Determine the base condition for this recurrence relation and determine by iteration a closed form formula for the value of the recurrence relation for any number of digits n. C) Prove that your formula is correct.

Name: Discrete mathematics a) Find a recurrence relation that would determin
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Description: Discrete mathematics a) Find a recurrence relation that would determine the number of sequences a1, a2, , anthat have an odd number of zeros when each a, E { 0, 1, 2 }, in terms of the number of sequences ofn-1 of these elements that do.For example w

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Student ID Math Score Project Score Age (years) Sex 001254 52 75 15 M 003256 78 89 15 F 001547 92 82 18 F 012589 91 66 17 M 021475 72 93 14 M 032658 46 76 13 M 009561 68 76 14 F 008654 52 82 12 F 008561 83 75 16 M 003547 45 78 14 F 047452 73 96 14 M 041212 64 79 13 F 032320 41 67 13 F 000258 77 72 15 F 001478 82 75 17 M 019521 59 83 15 M 017451 80 71 17 F 016335 48 76 13 M 002474 57 80 14 F 095844 97 71 18 F 097304 86 86 17 M 090024 75 85 15 F 034702 81 80 16 F 001910 67 74 14 F 006454 86 77 17 M 087478 63 82 13 M 078474 68 79 14 F 000977 54 89 12 M 063010 91 73 18 M 007406 46 77 15 F 025740 93 85 17 M…
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Male Female 27,767 20,516 17,413 24,972 6,080 4,900 28,523 17,661 25,137 11,901 9,821 17,562 21,857 9,865 16,491 21,047 27,687 12,095 23,361 20,089 12,272 16,244 9,584 14,395 13,562 15,467 23,151 23,501 20,071 5,715 142 19,698 21,957 21,640 8,722 18,345 21,058 16,616 17,940 15,249 15,001 28,849 20,938 6,825 6,151 17,111 8,370 4,197 27,687 12,989 11,589 16,879 12,021 13,322 13,709 20,292 12,888 19,417 17,879 14,061 13,743 32,349 11,268 8,738 22,102 10,475 16,788 11,971 10,387 28,702 13,809 22,947 15,644 16,386 11,044 20,101 17,933 20,564 11,413 14,483 11,842 17,349 6,794…
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Student ID Math Score Project Score Age (years) Sex 001254 52 75 15 M 003256 78 89 15 F 001547 92 82 18 F 012589 91 66 17 M 021475 72 93 14 M 032658 46 76 13 M 009561 68 76 14 F 008654 52 82 12 F 008561 83 75 16 M 003547 45 78 14 F 047452 73 96 14 M 041212 64 79 13 F 032320 41 67 13 F 000258 77 72 15 F 001478 82 75 17 M 019521 59 83 15 M 017451 80 71 17 F 016335 48 76 13 M 002474 57 80 14 F 095844 97 71 18 F 097304 86 86 17 M 090024 75 85 15 F 034702 81 80 16 F 001910 67 74 14 F 006454 86 77 17 M 087478 63 82 13 M 078474 68 79 14 F 000977 54 89 12 M 063010 91 73 18 M 007406 46 77 15 F 025740 93 85 17 M…