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A292045 Wiener index of the n X n X n grid graph. 0
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 (list; graph; refs; listen; history; text; internal format)
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 * A272778 A160068 A229387

Adjacent sequences:  A292042 A292043 A292044 * A292046 A292047 A292048

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Sep 08 2017

STATUS

approved

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Last modified October 15 12:31 EDT 2019. Contains 328026 sequences. (Running on oeis4.)