A242983 a(n) = (n/2) * (n^3 - 2*n^2 - 2*n + 5).

0, 1, 1, 12, 58, 175, 411, 826, 1492, 2493, 3925, 5896, 8526, 11947, 16303, 21750, 28456, 36601, 46377, 57988, 71650, 87591, 106051, 127282, 151548, 179125, 210301, 245376, 284662, 328483, 377175, 431086, 490576, 556017, 627793, 706300, 791946, 885151, 986347

Offset

0,4

Comments

For n>1, number of ways to place two dominoes horizontally on an n X n chessboard.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for sequences related to dominoes.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = A019582(n) + A077414(n-2), n>1.

G.f.: x*(-2*x^3 + 17*x^2 - 4*x + 1) / (1-x)^5.

E.g.f.: exp(x)*x*(2 - x + 4*x^2 + x^3)/2. - Stefano Spezia, Jan 21 2026

Mathematica

Table[n/2 (n^3-2n^2-2n+5), {n, 0, 40}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {0, 1, 1, 12, 58}, 40] (* Harvey P. Dale, Jul 19 2018 *)
CoefficientList[Series[x*(-2*x^3+17*x^2-4*x+1)/(1-x)^5, {x, 0, 35}], x] (* Vincenzo Librandi, Jan 20 2026 *)

Prog

(Magma) m := 35; R<x> := PowerSeriesRing(Integers(), m+1); f := x * (-2*x^3 + 17*x^2 - 4*x + 1) / (1 - x)^5; [ Coefficient(f, n) : n in [0..m] ]; // Vincenzo Librandi, Jan 20 2026

Crossrefs

Cf. A019582, A077414, A242856, A242861.

Sequence in context: A072259 A272233 A283164 * A167533 A244907 A374963

Adjacent sequences: A242980 A242981 A242982 * A242984 A242985 A242986

Keyword

nonn,easy

Author

Ralf Stephan, Jun 09 2014

Status

approved