A270869 a(n) = n^5 + 4*n^4 + 13*n^3 + 23*n^2 + 25*n + 3.

3, 69, 345, 1203, 3351, 7953, 16749, 32175, 57483, 96861, 155553, 239979, 357855, 518313, 732021, 1011303, 1370259, 1824885, 2393193, 3095331, 3953703, 4993089, 6240765, 7726623, 9483291, 11546253, 13953969, 16747995, 19973103, 23677401, 27912453

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Andrew Misseldine, Counting Schur Rings over Cyclic Groups, arXiv preprint arXiv:1508.03757 [math.RA], 2015. (page 19, 4th row; page 21, 5th row).

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

O.g.f.: (3 + 51*x - 24*x^2 + 108*x^3 - 27*x^4 + 9*x^5)/(1-x)^6.

E.g.f.: (3 + 66*x + 105*x^2 + 62*x^3 + 14*x^4 + x^5)*exp(x).

a(n) = 6*a(n-1) -15*a(n-2) +20*a(n-3) -15*a(n-4) +6*a(n-5) -a(n-6).

Mathematica

Table[n^5 + 4 n^4 + 13 n^3 + 23 n^2 + 25 n + 3, {n, 0, 40}]

Prog

(Magma) [n^5+4*n^4+13*n^3+23*n^2+25*n+3: n in [0..40]];
(PARI) x='x+O('x^99); Vec((3+51*x-24*x^2+108*x^3-27*x^4+9*x^5)/(1-x)^6) \\ Altug Alkan, Apr 03 2016

Crossrefs

Cf. A270867, A270868.

Sequence in context: A124181 A046432 A232326 * A241222 A166835 A166806

Adjacent sequences: A270866 A270867 A270868 * A270870 A270871 A270872

Keyword

nonn,easy

Author

Vincenzo Librandi, Apr 03 2016

Status

approved