A144109 INVERT transform of the cubes A000578.

1, 9, 44, 207, 991, 4752, 22769, 109089, 522676, 2504295, 11998799, 57489696, 275449681, 1319758713, 6323343884, 30296960703, 145161459631, 695510337456, 3332390227649, 15966440800785, 76499813776276, 366532628080599

Offset: 0

Author

R. J. Mathar, Sep 11 2008

Keywords

• nonn
• easy

Comments

Analog of A033453 (INVERT squares) and A001906 (INVERT first powers).

For n>1, a(n-1) is the number of generalized compositions of n when there are i^3 different types of i, (i=1,2,...). [Milan Janjic, Sep 24 2010]

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5, -2, 5, -1).

Crossrefs

Cf. A004254, A056594.

Programs

Mathematica

CoefficientList[Series[(1 + 4*x + x^2)/((1 + x^2)*(1 -5 *x + x^2)), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 14 2012 *)

Formula

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

a(n) = (9*A004254(n+1)-4*A056594(n))/5.