A329707 Number of placements of zero or more dominoes on a 2 X n grid where no two empty squares are horizontally adjacent.

1, 2, 4, 11, 25, 61, 146, 351, 844, 2028, 4875, 11717, 28163, 67692, 162703, 391070, 939968, 2259289, 5430383, 13052363, 31372406, 75406105, 181244648, 435636112, 1047086489, 2516756727, 6049227537, 14539805696, 34947594281, 83999358146, 201899224084, 485281049587, 1166412095721

Offset

0,2

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,1,0,0,0,-1).

Formula

a(n) = 2*a(n-1) + a(n-2) - a(n-6) for n > 6.

G.f.: (1 - x)*(1 + x + x^3)/(1 - 2*x - x^2 + x^6).

Mathematica

LinearRecurrence[{2, 1, 0, 0, 0, -1}, {1, 2, 4, 11, 25, 61}, 50] (* Paolo Xausa, Jun 19 2024 *)

Prog

(PARI) Vec((1 - x)*(1 + x + x^3)/(1 - 2*x - x^2 + x^6) + O(x^30))

Crossrefs

Row 2 of A332862.

Sequence in context: A342533 A131434 A100550 * A071973 A086424 A122121

Adjacent sequences: A329704 A329705 A329706 * A329708 A329709 A329710

Keyword

nonn

Author

Andrew Howroyd, Feb 28 2020

Status

approved