A270868 a(n) = n^4 + 3*n^3 + 8*n^2 + 9*n + 2.

2, 23, 92, 263, 614, 1247, 2288, 3887, 6218, 9479, 13892, 19703, 27182, 36623, 48344, 62687, 80018, 100727, 125228, 153959, 187382, 225983, 270272, 320783, 378074, 442727, 515348, 596567, 687038, 787439, 898472, 1020863, 1155362, 1302743, 1463804, 1639367

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, 5th row; page 21, 4th row).

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

G.f.: (2+13*x-3*x^2+13*x^3-x^4)/(1-x)^5.

a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5).

From G. C. Greubel, Apr 01 2016: (Start)

a(2*m) == 0 (mod 2).

a(4*m + 2) == 0 (mod 4).

E.g.f.: (2 +21*x +24*x^2 +9*x^3 +x^4)*exp(x). (End)

a(n)+a(n+2)-2*a(n+1) = 6*A033816(n+1). - Wesley Ivan Hurt, Apr 02 2016

Maple

A270868:=n->n^4 + 3*n^3 + 8*n^2 + 9*n + 2: seq(A270868(n), n=0..50); # Wesley Ivan Hurt, Apr 01 2016

Mathematica

Table[n^4 + 3 n^3 + 8 n^2 + 9 n + 2, {n, 0, 40}]

Prog

(Magma) [n^4+3*n^3+8*n^2+9*n+2: n in [0..40]];

Crossrefs

Cf. A033816, A270867.

Sequence in context: A069152 A131464 A245331 * A239186 A238185 A053999

Adjacent sequences: A270865 A270866 A270867 * A270869 A270870 A270871

Keyword

nonn,easy

Author

Vincenzo Librandi, Apr 01 2016

Status

approved