A153026 a(1)=0, a(n) = n^3 - a(n-1).

0, 8, 19, 45, 80, 136, 207, 305, 424, 576, 755, 973, 1224, 1520, 1855, 2241, 2672, 3160, 3699, 4301, 4960, 5688, 6479, 7345, 8280, 9296, 10387, 11565, 12824, 14176, 15615, 17153, 18784, 20520, 22355, 24301, 26352, 28520, 30799, 33201, 35720, 38368

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Dec 17 2008

Keywords

• nonn
• easy

Comments

The old name was: a(n)+a(n+1) = cube: 0+8=8=2^3; 8+19=27=3^3; 19+45=64=4^3; ...

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A125577, A153026.

Programs

Magma

[n le 1 select n-1 else n^3-Self(n-1): n in [1..50]]; // Vincenzo Librandi, May 19 2014

Mathematica

a=1;lst={};Do[a=n^3-a;AppendTo[lst,a],{n,1,5!}];lst
CoefficientList[Series[x (8 - 5 x + 4 x^2 - x^3)/((1 + x) (1 - x)^4), {x, 0, 50}], x] (* Vincenzo Librandi, May 19 2014 *)

Formula

From R. J. Mathar, Dec 19 2008: (Start)

G.f.: x^2*(8-5*x+4*x^2-x^3)/((1+x)*(1-x)^4).

a(n)+a(n+1) = A000578(n+1).

a(n)= -1/8+3*n^2/4+n^3/2+9*(-1)^n/8. (End)

Extensions

Name improved by Alex Ratushnyak, Aug 05 2012