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
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).
Programs
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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)];
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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 *) -
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
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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
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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
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