We want to tile an n × 1 strip with 1 × 1 tiles that are GREEN (G), BLUE (B), and RED (R), 2 × 1 PURPLE (P) and 2 × 1 ORANGE (O) tiles. GREEN, BLUE and PURPLE tiles cannot be next to each other, and there should be no two PURPLE or three BLUE or GREEN tiles in a row (for ex., GGOBR is allowed, but GGGOBR,GROPP and PBOBR are not). Give a formula for the number of such tilings. Your solution must include a recurrence equation (with initial conditions!), and a full justification. You do not need to solve it.
We want to tile an n × 1 strip with 1 × 1 tiles that are GREEN (G), BLUE (B), and RED (R), 2 × 1 PURPLE (P) and 2 × 1 ORANGE (O) tiles. GREEN, BLUE and PURPLE tiles cannot be next to each other, and there should be no two PURPLE or three BLUE or GREEN tiles in a row (for ex., GGOBR is allowed, but GGGOBR,GROPP and PBOBR are not). Give a formula for the number of such tilings. Your solution must include a recurrence equation (with initial conditions!), and a full justification. You do not need to solve it.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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We want to tile an n × 1 strip with 1 × 1 tiles that are GREEN (G), BLUE (B), and RED (R), 2 × 1
PURPLE (P) and 2 × 1 ORANGE (O) tiles.
GREEN, BLUE and PURPLE tiles cannot be next to each other, and
there should be no
two PURPLE or three BLUE or GREEN tiles in a row
(for ex., GGOBR is allowed, but GGGOBR,GROPP and PBOBR are not).
Give a formula for the number of such tilings. Your solution must include a recurrence equation (with initial conditions!), and a full justification. You do not need to solve it.
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