A288959 a(n) = n^2*(n^2 - 1)^2/2.

0, 18, 288, 1800, 7200, 22050, 56448, 127008, 259200, 490050, 871200, 1472328, 2384928, 3726450, 5644800, 8323200, 11985408, 16901298, 23392800, 31840200, 42688800, 56455938, 73738368, 95220000, 121680000, 154001250, 193179168, 240330888, 296704800, 363690450

Offset

1,2

Comments

Except for n = 2, gives the detour index of the n X n rook and rook complement graph.

Also the detour index of the n X n king and n X n queen graphs. - Eric W. Weisstein, Dec 16 2017

Links

Table of n, a(n) for n=1..30.

Eric Weisstein's World of Mathematics, Detour Index

Eric Weisstein's World of Mathematics, King Graph

Eric Weisstein's World of Mathematics, Queen Graph

Eric Weisstein's World of Mathematics, Rook Complement Graph

Eric Weisstein's World of Mathematics, Rook Graph

Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).

Formula

a(n) = n^2*(n^2 - 1)^2/2.

a(n) = 7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7).

G.f.: (-18*x^2*(1+x)*(1+8*x+x^2))/(-1+x)^7.

a(n) = 18 *A001249(n-2). - R. J. Mathar, Dec 17 2017

Mathematica

Table[n^2 (n^2 - 1)^2/2, {n, 20}]
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 18, 288, 1800, 7200, 22050, 56448}, 20]
CoefficientList[Series[-((18 x (1 + x) (1 + 8 x + x^2))/(-1 + x)^7), {x, 0, 20}], x]
18 Binomial[Range[0, 20] + 2, 3]^2 (* Eric W. Weisstein, Dec 20 2017 *)

Prog

(PARI) a(n) = n^2*(n^2-1)^2/2; \\ Altug Alkan, Dec 20 2017

Crossrefs

Sequence in context: A368526 A035119 A230235 * A294327 A286725 A226998

Adjacent sequences: A288956 A288957 A288958 * A288960 A288961 A288962

Keyword

nonn,easy

Author

Eric W. Weisstein, Jun 20 2017

Status

approved