A131472 a(n) = n^6 + n.

0, 2, 66, 732, 4100, 15630, 46662, 117656, 262152, 531450, 1000010, 1771572, 2985996, 4826822, 7529550, 11390640, 16777232, 24137586, 34012242, 47045900, 64000020, 85766142, 113379926, 148035912, 191103000, 244140650, 308915802

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

G.f.: 2*x*(1 + 26*x + 156*x^2 + 146*x^3 + 31*x^4)/(1 - x)^7. - R. J. Mathar, Nov 14 2007

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7); a(0)=0, a(1)=2, a(2)=66, a(3)=732, a(4)=4100, a(5)=15630, a(6)=46662. - Harvey P. Dale, May 03 2012

E.g.f.: exp(x)*x*(2 + 31*x + 90*x^2 + 65*x^3 + 15*x^4 + x^5). - Stefano Spezia, Oct 08 2022

Mathematica

Table[n^6+n, {n, 0, 60}] (* Vladimir Joseph Stephan Orlovsky, May 12 2011 *)
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 2, 66, 732, 4100, 15630, 46662}, 60] (* Harvey P. Dale, May 03 2012 *)

Prog

(Magma)[n^6+n: n in [0..30]]; // _Vincenzo Librandi+, Oct 01 2011

Crossrefs

Cf. A002378, A007531, A034262, A091940, A058895, A059826.

Sequence in context: A349108 A226409 A226338 * A098532 A159716 A157060

Adjacent sequences: A131469 A131470 A131471 * A131473 A131474 A131475

Keyword

nonn,easy

Author

Mohammad K. Azarian, Jul 27 2007

Status

approved