A251691 G.f.: G(F(x)) is a power series in x consisting entirely of positive integer coefficients such that G(F(x) - x^k) has negative coefficients for k>0, where G(x) = 1 + x*G(x)^3 is the g.f. of A001764 and F(x) is g.f. of A251690.

1, 1, 2, 4, 8, 17, 36, 78, 169, 370, 813, 1793, 3971, 8817, 19631, 43804, 97938, 219357, 492072, 1105398, 2486320, 5598805, 12620832, 28477139, 64311189, 145354456, 328772330, 744155150, 1685434388, 3819629781, 8661130303, 19649713303, 44601771038, 101285994072, 230110466746

Offset

0,3

Links

Paul D. Hanna, Table of n, a(n) for n = 0..120

Formula

G.f.: A(x) = 1 + x + 2*x^2 + 4*x^3 + 8*x^4 + 17*x^5 + 36*x^6 + 78*x^7 + 169*x^8 + 370*x^9 + 813*x^10 + 1793*x^11 + 3971*x^12 +...

such that A(x) = G(F(x)), where G(x) = 1 + x*G(x)^3 is the g.f. of A001764:

G(x) = 1 + x + 3*x^2 + 12*x^3 + 55*x^4 + 273*x^5 + 1428*x^6 + 7752*x^7 +...

and F(x) is the g.f. of A251690:

F(x) = x - x^2 - 2*x^3 - 2*x^4 - x^6 - 3*x^8 - 3*x^10 - 3*x^11 - 3*x^13 - 2*x^14 - 3*x^15 - x^16 - 2*x^17 - x^19 - 2*x^20 - 2*x^23 - 2*x^27 - 3*x^29 +...

Crossrefs

Cf. A251690, A001764.

Sequence in context: A262735 A190162 A275691 * A157904 A182901 A002845

Adjacent sequences: A251688 A251689 A251690 * A251692 A251693 A251694

Keyword

nonn

Author

Paul D. Hanna, Dec 31 2014

Status

approved