A251581 G.f. satisfies: A(x) = A(x^2 + 2*x^3)/(1-x).

1, 1, 2, 4, 6, 14, 26, 50, 104, 184, 342, 674, 1356, 2788, 5518, 10826, 21370, 42026, 83522, 167026, 332744, 656000, 1275546, 2467078, 4781642, 9309626, 18249534, 36020326, 71503892, 142624604, 285547086, 573206970, 1151765116, 2311859564, 4629326326, 9244819530, 18421964748, 36659214484

Offset

0,3

Comments

Conjecture: limit of a(n+1)/a(n) = 2.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..2800

Vaclav Kotesovec, Graph a(n+1)/a(n)

Example

G.f.: A(x) = 1 + x + 2*x^2 + 4*x^3 + 6*x^4 + 14*x^5 + 26*x^6 + 50*x^7 + ...
such that A(x) = A(x^2 + 2*x^3)/(1-x), where
A(x^2+2*x^3) = 1 + x^2 + 2*x^3 + 2*x^4 + 8*x^5 + 12*x^6 + 24*x^7 + 54*x^8 + 80*x^9 + 158*x^10 + 332*x^11 + 682*x^12 + 1432*x^13 + 2730*x^14 + 5308*x^15 + 10544*x^16 + 20656*x^17 + 41496*x^18 + ...

Mathematica

m = 38; A[_] = 1; Do[A[x_] = A[x^2 + 2 x^3]/(1-x) + O[x]^m // Normal, {m}]; CoefficientList[A[x], x] (* Jean-François Alcover, Nov 03 2019 *)

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, #binary(n)+1, A=subst(A, x, x^2+2*x^3)/(1-x +x*O(x^n))); polcoeff(A, n)}
for(n=0, 50, print1(a(n), ", "))

Crossrefs

Cf. A251572, A251582.

Sequence in context: A084685 A219042 A325868 * A151794 A181528 A251393

Adjacent sequences: A251578 A251579 A251580 * A251582 A251583 A251584

Keyword

nonn

Author

Paul D. Hanna, Jan 31 2015

Status

approved