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

0,2

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

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

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 *)

Crossrefs

Cf. A005408, A152204.

Sequence in context: A081661 A005103 A001978 * A077552 A171497 A024623

Adjacent sequences: A173280 A173281 A173282 * A173284 A173285 A173286

Keyword

nonn

Author

Gary W. Adamson, Feb 14 2010

Extensions

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

Status

approved