A226546 Number of squares in all tilings of a 3 X n rectangle using integer-sided square tiles.
0, 3, 12, 34, 98, 256, 654, 1625, 3964, 9533, 22662, 53373, 124728, 289572, 668514, 1535869, 3513614, 8008090, 18191184, 41200568, 93064834, 209710139, 471520566, 1058065647, 2369890254, 5299215579, 11830941840, 26375563624, 58722396932, 130576680919
Offset: 0
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (2,3,-2,-6,-4,-1).
Programs
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PARI
concat(0, Vec(x*(3 + 6*x + x^2) / (1 - x - 2*x^2 - x^3)^2 + O(x^30))) \\ Colin Barker, Jun 07 2020
Formula
G.f.: (x^2+6*x+3)*x/(x^3+2*x^2+x-1)^2.
a(n) = 2*a(n-1) + 3*a(n-2) - 2*a(n-3) - 6*a(n-4) - 4*a(n-5) - a(n-6) for n>5. - Colin Barker, Jun 07 2020