A135917 a(n) = (n^6 - 30*n^4 + 45*n^3 + 206*n^2 - 576*n + 384)/6.

0, 4, 112, 859, 3640, 11250, 28544, 63217, 126704, 235200, 410800, 682759, 1088872, 1676974, 2506560, 3650525, 5197024, 7251452, 9938544, 13404595, 17819800, 23380714, 30312832, 38873289, 49353680, 62083000, 77430704, 95809887, 117680584, 143553190

Offset

2,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 2..1000

Geir Ellingsrud and Stein Arild Strømme, Bott's formula and enumerative geometry, arXiv:alg-geom/9411005, 1994.

Geir Ellingsrud and Stein Arild Strømme, Bott's formula and enumerative geometry, J. Amer. Math. Soc. 9 (1996), 175-193.

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

Formula

G.f.: x^3*(-4 - 84*x - 159*x^2 + 161*x^3 - 29*x^4 - 5*x^5) / (x-1)^7. - Harvey P. Dale, Apr 23 2011

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) for n > 9. - Stefano Spezia, Sep 03 2018

Mathematica

Table[(n^6-30n^4+45n^3+206n^2-576n+384)/6, {n, 2, 40}] (* or *) CoefficientList[Series[(-4x-84x^2-159x^3+161x^4-29x^5-5x^6)/ (x-1)^7, {x, 0, 40}], x] (* Harvey P. Dale, Apr 23 2011 *)
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 4, 112, 859, 3640, 11250, 28544}, 40] (* Stefano Spezia, Sep 03 2018 *)

Prog

(Magma) [(n^6 - 30*n^4 + 45*n^3 + 206*n^2 - 576*n + 384)/6: n in [2..35]]; // Vincenzo Librandi, May 04 2011
(PARI) a(n) = (n^6 - 30*n^4 + 45*n^3 + 206*n^2 - 576*n + 384)/6; \\ Andrew Howroyd, Nov 06 2018

Crossrefs

Sequence in context: A202518 A212655 A181485 * A241798 A158450 A063406

Adjacent sequences: A135914 A135915 A135916 * A135918 A135919 A135920

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 07 2008

Status

approved