A173283 A(x) satisfies A005408(x) = A(x)/A(x^2), A005408 = odd numbers.

1, 3, 8, 16, 32, 56, 96, 152, 240, 360, 536, 768, 1096, 1520, 2096, 2824, 3792, 5000, 6568, 8496, 10960, 13960, 17728, 22264, 27896, 34624, 42872, 52640, 64504, 78464, 95248, 114856, 138256, 165448, 197640, 234832, 278592, 328920, 387744, 455064

Offset: 0

Author

Gary W. Adamson, Feb 14 2010

Keywords

• nonn

Comments

(1 + 3x + 5x^2 + 7x^3 + ...) = (1 + 3x + 8x^2 + 16x^3 + ...) / (1 + 3x^2 + 8x^4 + 16x^6 + ...).

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A005408, A152204.

Programs

Maple

A173283 := proc(n) option remember; if n = 0 then 1; else add(procname(l)*(2*n-4*l+1),l=0..n/2) ; end if; end proc: seq(A173283(n),n=0..60) ; # R. J. Mathar, Apr 01 2010

Mathematica

m = 40;
A[_] = 1;
Do[A[x_] = A[x^2] (1 + x)/(1 - x)^2 + O[x]^m // Normal, {m}];
CoefficientList[A[x], x] (* Jean-François Alcover, Feb 06 2020 *)

Formula

Given M = triangle A152204, odd numbers shifted down twice in every column > 0.

A173283 = lim_{n->inf} M^n, the left-shifted vector considered as a sequence.

a(n) = Sum_{t=0..n/2} (2*n - 4*t + 1)*a(t). - R. J. Mathar, Apr 01 2010

Extensions

More terms from R. J. Mathar, Apr 01 2010