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A073712
Self-convolution of A073711.
3
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
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
Sequence in context: A238590 A144120 A375401 * A157200 A255940 A167415
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