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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. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 15 10:45 EDT 2021. Contains 343909 sequences. (Running on oeis4.)