A229740 -id:A229740 - cp's OEIS frontend

A255500 a(n) = (p^9 + 5p^8 + 4p^7 - p^6 - 5p^5 + 2p^4)/6 where p is the n-th prime.

352, 9909, 698125, 12045817, 584190541, 2487920149, 25846158097, 68520305701, 367691205289, 2846113596901, 5135516500321, 24650159312557, 61346708983561, 93685639700269, 206700247118737, 602622774810109, 1567842813615901, 2110866318916741, 4876836410298997

Offset: 1

N. J. A. Sloane, Mar 13 2015

nonn

G. C. Greubel, Table of n, a(n) for n = 1..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. [DOI]

Cf. A229738, A229740, A255501.

Table[(p^9+5p^8+4p^7-p^6-5p^5+2p^4)/6,{p,Prime[Range[20]]}] (* Harvey P. Dale, May 23 2020 *)

from _future_ import division
from sympy import prime
A255500_list = []
for n in range(1,10**2):
    p = prime(n)
    A255500_list.append(p**4*(p*(p*(p*(p*(p + 5) + 4) - 1) - 5) + 2)//6)
# Chai Wah Wu, Mar 14 2015

def p(n): return nth_prime(n)
def A255500(n): return p(n)^4*(p(n)^5 +5*p(n)^4 +4*p(n)^3 -p(n)^2 -5*p(n) +2)/6
[A255500(n) for n in (1..30)] # G. C. Greubel, Sep 24 2021

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

Original entry on oeis.org

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

N. J. A. Sloane, Mar 13 2015

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).

Cf. A229740, A255500.

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)];

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 *)

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

# 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

[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

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

cp's OEIS Frontend

A255500 a(n) = (p^9 + 5p^8 + 4p^7 - p^6 - 5p^5 + 2p^4)/6 where p is the n-th prime.

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

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cp's OEIS Frontend

A255500 a(n) = (p^9 + 5*p^8 + 4*p^7 - p^6 - 5*p^5 + 2*p^4)/6 where p is the n-th prime.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Python

Sage

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

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Python

Sage

Formula

A255500 a(n) = (p^9 + 5p^8 + 4p^7 - p^6 - 5p^5 + 2p^4)/6 where p is the n-th prime.

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