A255501 a(n) = (n^9 + 5*n^8 + 4*n^7 - n^6 - 5*n^5 + 2*n^4)/6.

0, 1, 352, 9909, 107776, 698125, 3252096, 12045817, 37679104, 103495401, 256420000, 584190541, 1241471232, 2487920149, 4741917376, 8654360625, 15207694336, 25846158097, 42644120544, 68520305701, 107506720000, 165082149981, 248581222912, 367691205289

Offset

0,3

Links

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

L. Kaylor and D. Offner, Counting matrices over a finite field with all eigenvalues in the field, Involve, a Journal of Mathematics, Vol. 7 (2014), No. 5, 627-645, see Theorem 6.1. [DOI]

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Formula

a(n) = n^4 * (n^5 + 5*n^4 + 4*n^3 - n^2 - 5*n + 2)/6.

G.f.: x*(1 +342*x +6434*x^2 +24406*x^3 +24240*x^4 +5354*x^5 -242*x^6 -54*x^7 -x^8)/(1-x)^10. - Colin Barker, Mar 14 2015

E.g.f.: (x/6)* (6 +1050*x +8856*x^2 +17562*x^3 +12741*x^4 +4059*x^5 +606*x^6 +41*x^7 +x^8)*exp(x). - G. C. Greubel, Sep 24 2021

Maple

fp:=n->(n^9+5*n^8+4*n^7-n^6-5*n^5+2*n^4)/6;
[seq(fp(n), n=0..40)];

Mathematica

Table[n^4*(n^5 +5*n^4 +4*n^3 -n^2 -5*n +2)/6, {n, 0, 30}] (* G. C. Greubel, Sep 24 2021 *)

Prog

(Python)
# requires Python 3.2 or higher
from itertools import accumulate
A255501_list, m  = [0], [60480, -208320, 273840, -168120, 45420, -2712, -648, 62, -1, 0]
for _ in range(10**2):
....m = list(accumulate(m))
A255501_list.append(m[-1]) # Chai Wah Wu, Mar 14 2015
(PARI)
concat(0, Vec(x*(1 +342*x +6434*x^2 +24406*x^3 +24240*x^4 +5354*x^5 -242*x^6 -54*x^7 -x^8)/(1-x)^10 + O(x^100))) \\ Colin Barker, Mar 14 2015
(Sage) [n^4*(n^5 +5*n^4 +4*n^3 -n^2 -5*n +2)/6 for n in (0..30)] # G. C. Greubel, Sep 24 2021

Crossrefs

Cf. A229740, A255500.

Sequence in context: A256025 A256771 A256764 * A229740 A255500 A256763

Adjacent sequences: A255498 A255499 A255500 * A255502 A255503 A255504

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 13 2015

Status

approved