A038376 a(n) = (n-3)*A006918(n-2)/2 for n >= 2, with a(0) = a(1) = 0.

0, 0, 0, 0, 1, 5, 12, 28, 50, 90, 140, 220, 315, 455, 616, 840, 1092, 1428, 1800, 2280, 2805, 3465, 4180, 5060, 6006, 7150, 8372, 9828, 11375, 13195, 15120, 17360, 19720, 22440, 25296, 28560, 31977, 35853, 39900, 44460, 49210, 54530, 60060, 66220, 72611

Offset

0,6

References

K. B. Reid and L. W. Beineke "Tournaments", pp. 169-204 in L. W. Beineke and R. J. Wilson, editors, Selected Topics in Graph Theory, Academic Press, NY, 1978, p. 186 Theorem 6.11.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,2,-6,0,6,-2,-2,1).

Formula

From Colin Barker, Nov 19 2016: (Start)

a(n) = (n^4-3*n^3-4*n^2+12*n)/48 for n even.

a(n) = (n^4-3*n^3-n^2+3*n)/48 for n odd.

a(n) = 2*a(n-1) + 2*a(n-2) - 6*a(n-3) + 6*a(n-5) - 2*a(n-6) - 2*a(n-7) + a(n-8) for n>7.

G.f.: x^4*(1+3*x) / ((1-x)^5 * (1+x)^3). (End)

a(n) = n*(n - 3)*(2*n^2 - 3*(-1)^n - 5)/96. - Paolo Xausa, Sep 17 2024 (derived from Bruno Berselli formula in A006918)

Mathematica

LinearRecurrence[{2, 2, -6, 0, 6, -2, -2, 1}, {0, 0, 0, 0, 1, 5, 12, 28}, 100]
(* or *)
A038376[n_] := n*(n - 3)*(2*n^2 - 3*(-1)^n - 5)/96;
Array[A038376, 100, 0] (* Paolo Xausa, Sep 16 2024 *)

Prog

(PARI) concat(vector(4), Vec(x^4*(1+3*x) / ((1-x)^5 * (1+x)^3) + O(x^100))) \\ Colin Barker, Nov 19 2016

Crossrefs

Cf. A006918.

Sequence in context: A145768 A162778 A160807 * A002767 A055245 A196410

Adjacent sequences: A038373 A038374 A038375 * A038377 A038378 A038379

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Name corrected by Paolo Xausa, Sep 16 2024

Status

approved