A292282 a(n) = 2*(n-1)^3*n^2*(n+1).

0, 24, 576, 4320, 19200, 63000, 169344, 395136, 829440, 1603800, 2904000, 4983264, 8176896, 12918360, 19756800, 29376000, 42614784, 60488856, 84214080, 115231200, 155232000, 206186904, 270374016, 350409600, 449280000, 570375000, 717522624, 895025376, 1107697920

Offset

1,2

Comments

Molecular topological index of the n X n rook complement graph for n != 2.

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Eric Weisstein's World of Mathematics, Molecular Topological Index.

Eric Weisstein's World of Mathematics, Rook Complement Graph.

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

Formula

a(n) = 2*(n-1)^3*n^2*(n+1).

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.: -24*x^2*(1 + 17*x + 33*x^2 + 9*x^3)/(-1 + x)^7.

From Amiram Eldar, Apr 16 2022: (Start)

Sum_{n>=2} 1/a(n) = 51/32 - 3*Pi^2/16 + zeta(3)/4.

Sum_{n>=2} (-1)^n/a(n) = 2*log(2) + 3*zeta(3)/16 - 47/32 - Pi^2/96. (End)

Mathematica

Table[2 (-1 + n)^3 n^2 (1 + n), {n, 20}]
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 24, 576, 4320, 19200, 63000, 169344}, 30]
CoefficientList[Series[-24 x (1 + 17 x + 33 x^2 + 9 x^3)/(-1 + x)^7, {x, 0, 20}], x]

Prog

(PARI) a(n)=2*(n-1)^3*n^2*(n+1) \\ Charles R Greathouse IV, Sep 14 2017
(Magma) [2*(n-1)^3*n^2*(n+1): n in [1..30]]; // G. C. Greubel, Dec 12 2017

Crossrefs

Sequence in context: A059061 A359751 A206991 * A206933 A206868 A181221

Adjacent sequences: A292279 A292280 A292281 * A292283 A292284 A292285

Keyword

nonn,easy

Author

Eric W. Weisstein, Sep 14 2017

Status

approved