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

0,2

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).

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

Prog

(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

Crossrefs

Column k=3 of A226545.

Cf. A002478.

Sequence in context: A257890 A060298 A304975 * A073372 A305023 A026573

Adjacent sequences: A226543 A226544 A226545 * A226547 A226548 A226549

Keyword

nonn,easy

Author

Alois P. Heinz, Jun 10 2013

Status

approved