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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
Eric Weisstein's World of Mathematics, Johnson Graph.
Eric Weisstein's World of Mathematics, Tetrahedral Graph.
Eric Weisstein's World of Mathematics, Wiener Index.
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: A361387 A256442 A296317 * A074441 A006741 A120573
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Sep 08 2017
STATUS
approved

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Last modified March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)