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 A244281 Answer to Red, Green and Blue Tiles Problem. 0
 0, 0, 1, 4, 11, 23, 43, 75, 126, 207, 335, 536, 852, 1350, 2136, 3378, 5344, 8462, 13416, 21300, 33866, 53923, 85979, 137274, 219444, 351203, 562667, 902327, 1448298, 2326472, 3739820, 6015701, 9682260, 15591825, 25120251, 40489004, 65285631, 105304917, 169908475 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS A row of n black squares is to have a number of its squares replaced by rectangles of lengths 2 (red), 3 (green) or 4 (blue). In how many different ways can the original squares be replaced if rectangles cannot be mixed and at least one rectangle must be used? LINKS Table of n, a(n) for n=0..38. Kristian Edlund, MathBlog, Project Euler 116: Investigating the number of ways of replacing square tiles with one of three coloured tiles. Project Euler, Problem 116: Red, green or blue tiles FORMULA Empirical g.f.: -x^2*(3*x^7+2*x^6+x^4-3*x^3-x+1) / ((x-1)^2*(x^2+x-1)*(x^3+x-1)*(x^4+x-1)). - Colin Barker, Nov 14 2014 PROG (Python) import math for n in range(1, 40): ans = 0 for k in range(0, n): for i in range(2, 5): for j in range(1, ((k/i)+1)): c = k - (i * j) + j ans = ans + (math.factorial(c) / (math.factorial(j) * math.factorial(k-(i*j)))) print ans CROSSREFS Sequence in context: A019298 A237586 A173702 * A014242 A240074 A008181 Adjacent sequences: A244278 A244279 A244280 * A244282 A244283 A244284 KEYWORD nonn AUTHOR Jameson Lee, Jul 02 2014 STATUS approved

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Last modified June 3 10:18 EDT 2023. Contains 363107 sequences. (Running on oeis4.)