A229738 -id:A229738 - cp's OEIS frontend

A255499 a(n) = (n^4 + 2*n^3 - n^2)/2.

0, 1, 14, 63, 184, 425, 846, 1519, 2528, 3969, 5950, 8591, 12024, 16393, 21854, 28575, 36736, 46529, 58158, 71839, 87800, 106281, 127534, 151823, 179424, 210625, 245726, 285039, 328888, 377609, 431550, 491071, 556544, 628353, 706894, 792575, 885816, 987049, 1096718, 1215279, 1343200

Offset: 0

N. J. A. Sloane, Mar 13 2015

G. C. Greubel, 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, DOI: 10.2140/involve.2014.7.627; see Eq. (1).
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Cf. A229738.

[n^4/2+n^3-n^2/2: n in [0..40]] // Vincenzo Librandi, Sep 05 2015

Table[n^4/2 + n^3 - n^2/2, {n, 0, 60}] (* or *) CoefficientList[Series[x (1 + 9 x + 3 x^2 - x^3)/(1 - x)^5, {x, 0, 45}], x] (* Vincenzo Librandi, Sep 05 2015 *)
LinearRecurrence[{5,-10,10,-5,1},{0,1,14,63,184},50] (* Harvey P. Dale, Nov 11 2017 *)

a(n) = n^4/2+n^3-n^2/2; \\ Michel Marcus, Sep 05 2015

[n^2*(n^2 +2*n -1)/2 for n in (0..40)] # G. C. Greubel, Sep 24 2021

G.f.: x*(1+9*x+3*x^2-x^3)/(1-x)^5. - Vincenzo Librandi, Sep 05 2015
a(n) = 5*a(n-1) -10*a(n-2) +10*a(n-3) -5*a(n-4) +a(n-5). - Vincenzo Librandi, Sep 05 2015
a(n) = Sum_{k=n..n+n^2-1} k (the sum of the first n^2 integers starting with n). - Matthew Niemiro, Jun 26 2020
E.g.f.: (x/2)*(2 +12*x +8*x^2 +x^3)*exp(x). - G. C. Greubel, Sep 24 2021

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

Original entry on oeis.org

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

A229739 a(n) = q^2(q^2+2q-1)/2, where q = n-th prime power A000961(n).

Original entry on oeis.org

1, 14, 63, 184, 425, 1519, 2528, 3969, 8591, 16393, 36736, 46529, 71839, 151823, 210625, 285039, 377609, 491071, 556544, 987049, 1480961, 1787983, 2542559, 2998849, 4092713, 6262319, 7148041, 8648704, 10374079, 13061231, 14585473, 19964959, 22051521, 24297503, 32072129, 45172609, 53055401, 57362863, 66759119

Offset: 1

N. J. A. Sloane, Oct 05 2013

nonn

L. Kaylor, 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. A000961, A229738.

A229740 a(n) = q^9/6+5q^8/6+2q^7/3-q^6/6-5*q^5/6+q^4/3 where q = n-th prime power A000961(n).

Original entry on oeis.org

1, 352, 9909, 107776, 698125, 12045817, 37679104, 103495401, 584190541, 2487920149, 15207694336, 25846158097, 68520305701, 367691205289, 766959765625, 1513188079677, 2846113596901, 5135516500321, 6803021627392, 24650159312557, 61346708983561, 93685639700269, 206700247118737, 299545983486001

Offset: 1

N. J. A. Sloane, Oct 05 2013

nonn

L. Kaylor, 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. A000961, A229738, A229739, A255500, A255501.

cp's OEIS Frontend

A255499 a(n) = (n^4 + 2*n^3 - n^2)/2.

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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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A229739 a(n) = q^2(q^2+2q-1)/2, where q = n-th prime power A000961(n).

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A229740 a(n) = q^9/6+5q^8/6+2q^7/3-q^6/6-5*q^5/6+q^4/3 where q = n-th prime power A000961(n).

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cp's OEIS Frontend

A255499 a(n) = (n^4 + 2*n^3 - n^2)/2.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Sage

Formula

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

A229739 a(n) = q^2*(q^2+2*q-1)/2, where q = n-th prime power A000961(n).

Views

Author

Keywords

Links

Crossrefs

A229740 a(n) = q^9/6+5*q^8/6+2*q^7/3-q^6/6-5*q^5/6+q^4/3 where q = n-th prime power A000961(n).

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

A229739 a(n) = q^2(q^2+2q-1)/2, where q = n-th prime power A000961(n).

A229740 a(n) = q^9/6+5q^8/6+2q^7/3-q^6/6-5*q^5/6+q^4/3 where q = n-th prime power A000961(n).