A337024 Number of ways to tile a 2n X 2n square with 1 X 1 white and n X n black squares.
16, 35, 60, 91, 128, 171, 220, 275, 336, 403, 476, 555, 640, 731, 828, 931, 1040, 1155, 1276, 1403, 1536, 1675, 1820, 1971, 2128, 2291, 2460, 2635, 2816, 3003, 3196, 3395, 3600, 3811, 4028, 4251, 4480, 4715, 4956, 5203
Offset: 1
Examples
For example, here are two of the 35 ways to tile a 4 X 4 square with 1 X 1 and 2 X 2 squares (where we have dropped the colors): ._______ _______ |_|_| | |_|_| | | |___| |_|_|___| |___| | | | | |_|_|___| |_ _|___|
Links
- R. J. Mathar, Tiling n x m rectangles with 1 x 1 and s x s squares, arXiv:1609.03964 [math.CO], 2016, Section 4.1.
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Crossrefs
Cf. A063443.
Programs
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Mathematica
Table[3 n^2 + 10 n + 3, {n, 50}] (* Wesley Ivan Hurt, Nov 07 2020 *)
Formula
a(n) = 3*n^2 + 10*n + 3.
From Stefano Spezia, Aug 18 2020: (Start)
O.g.f.: x*(16 - 13*x + 3*x^2)/(1 - x)^3.
E.g.f.: exp(x)*(3 + 13*x + 3*x^2) - 3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)
Extensions
Edited by Greg Dresden, Aug 18 2020