A135923 (n^8 - 60*n^6 + 90*n^5 + 1160*n^4 - 3204*n^3 - 5349*n^2 + 26586*n - 23760)/24.

0, 35, 1430, 13941, 75205, 289800, 897165, 2379300, 5620846, 12135825, 24377000, 46145495, 83119995, 143526526, 238971495, 385462350, 604641900, 925264015, 1384940106, 2032187465, 2928812225, 4152661380, 5800779985, 7993011336, 10876079610, 14628196125

Offset

3,2

Links

Chai Wah Wu, Table of n, a(n) for n = 3..1000

Ellingsrud, Geir and Stromme, Stein Arild, Bott's formula and enumerative geometry, J. Amer. Math. Soc. 9 (1996), 175-193. [arXiv:alg-geom/9411005]

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Formula

a(n) = (n-3)*(n+6)*(n^6-3*n^5-33*n^4+135*n^3+161*n^2-1257*n+1320)/24 .

a(n)=9*a(n-1)-36*a(n-2)+ 84*a(n-3)-126*a(n-4)+126*a(n-5)-84*a(n-6)+36*a(n-7)-9*a(n-8)+a(n-9), n>=12 [Harvey P. Dale, Oct 20 2011]

G.f.: x^4*(-10*x^7 +279*x^6 -1071*x^5 +879*x^4 +1724*x^3 -2331*x^2 -1115*x - 35)/(x-1)^9 [Harvey P. Dale, Oct 20 2011]

Mathematica

Table[(n^8-60n^6+90n^5+1160n^4-3204n^3-5349n^2+26586n-23760)/24, {n, 3, 30}] (* or *) LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {0, 35, 1430, 13941, 75205, 289800, 897165, 2379300, 5620846}, 30] (* Harvey P. Dale, Oct 20 2011 *)

Prog

(Python)
from itertools import islice
def A135923_generator():
....m = [1680, -840, -1380, -240, 641, 393, -209, -10, 0]
....yield m[-1]
....while True:
........for i in range(8):
............m[i+1]+= m[i]
........yield m[-1]
list(islice(A135923_generator(), 0, 50, 1)) # Chai Wah Wu, Nov 14 2014

Crossrefs

Sequence in context: A029560 A195617 A249885 * A180883 A130005 A199362

Adjacent sequences: A135920 A135921 A135922 * A135924 A135925 A135926

Keyword

nonn

Author

N. J. A. Sloane, Mar 07 2008

Status

approved