A132330 G.f.: A(x) = 1 + x*(A_2)^3; A_2 = 1 + x^2*(A_3)^3; A_3 = 1 + x^3*(A_4)^3; ... A_n = 1 + x^n*(A_{n+1})^3 for n>=1 with A_1 = A(x).

1, 1, 0, 3, 0, 3, 9, 1, 18, 9, 36, 45, 57, 90, 114, 351, 165, 558, 738, 1044, 1791, 1908, 3915, 4926, 8568, 8553, 17217, 26271, 30474, 50967, 68526, 113319, 144324, 219195, 299359, 473454, 665424, 860733, 1396350, 1895913, 2762550, 3790935, 5695974

Offset

0,4

Links

Table of n, a(n) for n=0..42.

Formula

G.f. A(x) = B(x,x), where B(w,x) satisfies the functional equation B(w,x) = 1 + x*B(w,wx)^3. B(w,x) is the g.f. for the number of ternary trees of given path length and number of nodes; B(1,x) is the g.f. for A001764.

Prog

(PARI) {a(n)=local(A=1+x*O(x^n)); for(j=0, n-1, A=1+x^(n-j)*A^3); polcoeff(A, n)}

Crossrefs

Cf. A132331 (cube); A001764; A108643 (variant).

Sequence in context: A099093 A137339 A230184 * A117078 A021333 A348670

Adjacent sequences: A132327 A132328 A132329 * A132331 A132332 A132333

Keyword

nonn

Author

Paul D. Hanna, Aug 20 2007

Status

approved