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A292061 a(n) = (n-3)*(n-2)^2*(n-1)^2*n/24. 0
0, 0, 0, 6, 60, 300, 1050, 2940, 7056, 15120, 29700, 54450, 94380, 156156, 248430, 382200, 571200, 832320, 1186056, 1656990, 2274300, 3072300, 4091010, 5376756, 6982800, 8970000, 11407500, 14373450, 17955756, 22252860, 27374550, 33442800, 40592640, 48973056, 58747920 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Wiener index of the n-tetrahedral graph for n >= 6.

LINKS

Table of n, a(n) for n=1..35.

Eric Weisstein's World of Mathematics, Johnson Graph.

Eric Weisstein's World of Mathematics, Tetrahedral Graph.

Eric Weisstein's World of Mathematics, Wiener Index.

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

FORMULA

a(n) = (n - 3)*(n - 2)^2*(n - 1)^2*n/24.

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.: -6*x^4*(1 + 3*x + x^2)/(-1 + x)^7.

From Amiram Eldar, Apr 16 2022: (Start)

Sum_{n>=4} 1/a(n) = 119/3 - 4*Pi^2.

Sum_{n>=4} (-1)^n/a(n) = 67/3 - 32*log(2). (End)

MATHEMATICA

Table[(n - 3) (n - 2)^2 (n - 1)^2 n/24, {n, 20}]

LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 0, 0, 6, 60, 300, 1050}, 20]

CoefficientList[Series[-((6 x^3 (1 + 3 x + x^2))/(-1 + x)^7), {x, 0, 20}], x]

CROSSREFS

Sequence in context: A069072 A256442 A296317 * A074441 A006741 A120573

Adjacent sequences:  A292058 A292059 A292060 * A292062 A292063 A292064

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Sep 08 2017

STATUS

approved

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Last modified October 6 20:00 EDT 2022. Contains 357270 sequences. (Running on oeis4.)