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 A091190 G.f. A(x) satisfies xA(x)^3 = B(xA(x^3)) where B(x) = x/(1-3x). 2
 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 MATHEMATICA m = 28; B[x_] = x/(1 - 3 x); A[_] = 1; Do[A[x_] = (B[x A[x^3]]/x)^(1/3) + O[x]^m // Normal, {m}]; CoefficientList[A[x], x] (* Jean-François Alcover, Oct 29 2019 *) 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: A005773 A307789 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 August 3 01:55 EDT 2021. Contains 346429 sequences. (Running on oeis4.)