A292045 Wiener index of the n X n X n grid graph.

0, 48, 972, 7680, 37500, 136080, 403368, 1032192, 2361960, 4950000, 9663060, 17791488, 31188612, 52437840, 85050000, 133693440, 204459408, 305165232, 445697820, 638400000, 898502220, 1244602128, 1699194552, 2289254400, 3046875000, 4009964400, 5223002148

Offset

1,2

Links

Table of n, a(n) for n=1..27.

Eric Weisstein's World of Mathematics, Grid Graph

Eric Weisstein's World of Mathematics, Wiener Index

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Formula

a(n) = (n - 1)*(n + 1)*n^5/2.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8).

G.f.: 12*x^2*(4 + 49*x + 104*x^2 + 49*x^3 + 4*x^4)/(1 - x)^8.

Mathematica

Table[(n - 1) (n + 1) n^5/2, {n, 20}]
LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {0, 48, 972, 7680, 37500, 136080, 403368, 1032192}, 20]
CoefficientList[Series[12 x (4 + 49 x + 104 x^2 + 49 x^3 + 4 x^4)/(1 - x)^8, {x, 0, 20}], x]

Crossrefs

Sequence in context: A293778 A089903 A274806 * A341306 A272778 A160068

Adjacent sequences: A292042 A292043 A292044 * A292046 A292047 A292048

Keyword

nonn,easy

Author

Eric W. Weisstein, Sep 08 2017

Status

approved