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A091190 G.f. A(x) satisfies xA(x)^3 = B(xA(x^3)) where B(x) = x/(1-3x). 3
1, 1, 2, 5, 13, 35, 97, 273, 778, 2240, 6499, 18976, 55703, 164243, 486130, 1443620, 4299365, 12836825, 38413933, 115184282, 346005073, 1041072108, 3137060983, 9465689545, 28596915843, 86492865522, 261876842801, 793661873276 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

More generally, given A(x) satisfies xA(x)^p = B(xA(x^p)) where B(x) = x/(1-p*x), then it appears that A(x) is an integer series only when p is prime. This is a special case of sequences with g.f.s that satisfy the more general functional equation xA(x)^m = B(xA(x^m)) originated by Michael Somos; some other examples are A085748, A091188 and A091200.

LINKS

Table of n, a(n) for n=0..27.

PROG

(PARI) {a(n)=local(A, m); p=3; if(n<0, 0, m=1; A=1+O(x); while(m<=n, m*=p; A=x*subst(A, x, x^p); A=(A/(1-p*A)/x)^(1/p)); polcoeff(A, n))}

CROSSREFS

Cf. A085748, A091188, A091200.

Sequence in context: A235611 A005773 A022855 * A264228 A007689 A085281

Adjacent sequences:  A091187 A091188 A091189 * A091191 A091192 A091193

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Feb 22 2004

EXTENSIONS

Corrected by T. D. Noe, Oct 25 2006

STATUS

approved

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Last modified October 19 07:56 EDT 2018. Contains 316337 sequences. (Running on oeis4.)