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