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A337024
Number of ways to tile a 2n X 2n square with 1 X 1 white and n X n black squares.
1
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
1,1
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)
EXAMPLE
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):
._______ _______
|_|_| | |_|_| |
| |___| |_|_|___|
|___| | | | |
|_|_|___| |_ _|___|
MATHEMATICA
Table[3 n^2 + 10 n + 3, {n, 50}] (* Wesley Ivan Hurt, Nov 07 2020 *)
CROSSREFS
Cf. A063443.
Sequence in context: A294073 A086119 A105509 * A219316 A317818 A236463
KEYWORD
nonn,easy
AUTHOR
Yutong Li, Aug 11 2020
EXTENSIONS
Edited by Greg Dresden, Aug 18 2020
STATUS
approved