A071244 a(n) = n*(n-1)*(n^2 + 2)/6.

0, 0, 2, 11, 36, 90, 190, 357, 616, 996, 1530, 2255, 3212, 4446, 6006, 7945, 10320, 13192, 16626, 20691, 25460, 31010, 37422, 44781, 53176, 62700, 73450, 85527, 99036, 114086, 130790, 149265, 169632, 192016, 216546, 243355, 272580, 304362, 338846, 376181

Offset: 0

Author

N. J. A. Sloane, Jun 12 2002

Keywords

• nonn
• easy

References

• T. A. Gulliver, Sequences from Arrays of Integers, Int. Math. Journal, Vol. 1, No. 4, pp. 323-332, 2002.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..2000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A071239.

Programs

Magma

[n*(n-1)*(n^2+2)/6: n in [0..40]]; // Vincenzo Librandi, Jun 14 2011

Mathematica

Table[n(n-1)(n^2+2)/6,{n,0,50}] (* or *) LinearRecurrence[{5,-10,10,-5,1},{0,0,2,11,36},50] (* Harvey P. Dale, Nov 27 2022 *)

PARI

a(n)=n*(n-1)*(n^2+2)/6; \\ Joerg Arndt, Sep 04 2013

SageMath

def A071244(n): return binomial(n,2)*(n^2+2)//3
[A071244(n) for n in range(41)] # G. C. Greubel, Aug 06 2024

Formula

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5), n > 4, a(0)=0, a(1)=0, a(2)=2, a(3)=11, a(4)=36. - Yosu Yurramendi, Sep 03 2013

From G. C. Greubel, Aug 06 2024: (Start)

G.f.: x^2*(2 + x + x^2)/(1 - x)^5.

E.g.f.: (1/6)*x^2*(6 + 5*x + x^2)*exp(x). (End)