A073712 Self-convolution of A073711.

1, 2, 3, 6, 7, 12, 16, 26, 31, 42, 59, 72, 104, 116, 184, 186, 303, 282, 497, 406, 783, 612, 1224, 840, 1856, 1232, 2784, 1656, 4136, 2376, 6008, 3138, 8735, 4362, 12345, 5754, 17693, 7756, 24432, 10170, 34471, 13302, 46771, 17688, 65144, 22296, 87008

Offset

0,2

Comments

The g.f. G(x) of A073711 satisfies: G(x) = G(x^2) + x*G(x^2)^2.

The terms of this sequence found at odd-indexed positions are equal to twice that of A194279, which equals the self-convolution cube of A073711.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Formula

a(n) = A073711(2*n+1) for n>=0.

a(2*n+1) = 2*A194279(n) for n>=0, where A194279 equals the self-convolution cube of A073711.

Mathematica

nmax = 46; max = 2*nmax+1; f[x_] := Sum[ a[k]*x^k, {k, 0, max}]; a[0] = a[1] = a[2] = 1; coes = CoefficientList[ Series[ f[x] - f[x^2] - x*f[x^2]^2, {x, 0, max}], x]; sol = Solve[ Thread[ coes == 0]] // First; Table[ a[2*n+1], {n, 0, nmax}] /. sol (* Jean-François Alcover, Mar 06 2013 *)

Prog

(Haskell)
a073712 n = a073712_list !! n
a073712_list = map (g a073711_list) [1..] where
g xs k = sum $ zipWith (*) xs $ reverse $ take k xs
-- Reinhard Zumkeller, Dec 20 2012
(PARI) a(n)=local(A=1); for(i=0, #binary(n), A=subst(A, x, x^2+x*O(x^n))+x*subst(A, x, x^2+x*O(x^n))^2); polcoeff(A^2, n)
for(n=0, 65, print1(a(n), ", ")) \\ Paul D. Hanna, Dec 21 2012

Crossrefs

Cf. A073711, A194279.

Sequence in context: A238590 A144120 A375401 * A157200 A255940 A167415

Adjacent sequences: A073709 A073710 A073711 * A073713 A073714 A073715

Keyword

easy,nice,nonn,look

Author

Paul D. Hanna, Aug 05 2002

Extensions

Name changed and entry revised by Paul D. Hanna, Dec 21 2012

Status

approved