A033562 a(n) = 2*n^3 + 1.

1, 3, 17, 55, 129, 251, 433, 687, 1025, 1459, 2001, 2663, 3457, 4395, 5489, 6751, 8193, 9827, 11665, 13719, 16001, 18523, 21297, 24335, 27649, 31251, 35153, 39367, 43905, 48779, 54001, 59583, 65537, 71875, 78609, 85751, 93313, 101307, 109745, 118639, 128001

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

A058895(n)^3 + A068601(n)^3 + a(n)^3 = A185065(n)^3, for n>0. - Vincenzo Librandi, Mar 13 2012

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. A058895, A068601, A185065.

Programs

GAP

List([0..50], n-> 2*n^3+1); # G. C. Greubel, Oct 12 2019

Magma

[2*n^3+1: n in [0..50]]; // G. C. Greubel, Oct 12 2019

Maple

seq(2*n^3+1, n=0..50); # G. C. Greubel, Oct 12 2019

Mathematica

2*Range[0,50]^3+1 (* Vladimir Joseph Stephan Orlovsky, Feb 14 2011*)
CoefficientList[Series[1+x*(3+5x+5x^2-x^3)/(1-x)^4,{x,0,40}],x] (* Vincenzo Librandi, Mar 13 2012 *)
LinearRecurrence[{4,-6,4,-1},{1,3,17,55},50] (* Harvey P. Dale, Aug 14 2023 *)

PARI

a(n)=2*n^3+1 \\ Charles R Greathouse IV, Mar 11 2012

Sage

[2*n^3+1 for n in range(50)] # G. C. Greubel, Oct 12 2019

Formula

G.f.: 1 + x*(3 + 5*x + 5*x^2 - x^3)/(1-x)^4. - Vincenzo Librandi, Mar 13 2012

E.g.f.: (1 + 2*x + 6*x^2 + 2*x^3)*exp(x). - G. C. Greubel, Oct 12 2019

Extensions

Terms a(34) onward added by G. C. Greubel, Oct 12 2019