A251691 - OEIS

%I #9 Jan 03 2015 03:28:53

%S 1,1,2,4,8,17,36,78,169,370,813,1793,3971,8817,19631,43804,97938,

%T 219357,492072,1105398,2486320,5598805,12620832,28477139,64311189,

%U 145354456,328772330,744155150,1685434388,3819629781,8661130303,19649713303,44601771038,101285994072,230110466746

%N 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.

%H Paul D. Hanna, <a href="/A251691/b251691.txt">Table of n, a(n) for n = 0..120</a>

%F 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 +...

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

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

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

%F 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 +...

%Y Cf. A251690, A001764.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Dec 31 2014