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

Author

Eric W. Weisstein, Jun 20 2017

Keywords

• nonn
• easy

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

• 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).

Programs

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 *)

PARI

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

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