A153057 a(0)=3; a(n) = n^2 + a(n-1) for n>0.

3, 4, 8, 17, 33, 58, 94, 143, 207, 288, 388, 509, 653, 822, 1018, 1243, 1499, 1788, 2112, 2473, 2873, 3314, 3798, 4327, 4903, 5528, 6204, 6933, 7717, 8558, 9458, 10419, 11443, 12532, 13688, 14913, 16209, 17578, 19022, 20543, 22143, 23824, 25588

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, Dec 17 2008

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A000330, A056520, A153056, A153058, A179904.

Programs

Magma

I:=[3,4,8,17]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..60]]; // Vincenzo Librandi, May 09 2017

Mathematica

a=3;lst={};Do[a=n^2+a;AppendTo[lst,a],{n,0,5!}];lst
CoefficientList[Series[(3 - 8 x + 10 x^2 - 3 x^3) / (1 - x)^4, {x, 0, 50}], x] (* Vincenzo Librandi, May 09 2017 *)

Formula

From R. J. Mathar, Jan 17 2009: (Start)

G.f.: (3-8*x + 10*x^2 - 3*x^3)/(1 - x)^4.

a(n) = 3+A000330(n). (End)

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Vincenzo Librandi, May 09 2017

Extensions

Added indices to definition. Corrected offset R. J. Mathar, Jan 17 2009