A251582 G.f. satisfies: A(x) = A(2*x^2 + x^3)/(1-x).

1, 1, 3, 4, 16, 28, 63, 111, 391, 907, 2187, 4555, 10843, 24059, 53667, 113503, 291971, 755271, 1951470, 4751194, 11609612, 27858363, 66082059, 152816667, 355501570, 832148914, 1961821400, 4601053219, 10765373983, 25089663963, 58267298334, 134371615378, 311517418324, 733798887871

Offset

0,3

Comments

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

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..2600

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

Example

G.f.: A(x) = 1 + x + 3*x^2 + 4*x^3 + 16*x^4 + 28*x^5 + 63*x^6 + 111*x^7 +...
such that A(x) = A(2*x^2 + x^3)/(1-x), where:
A(2*x^2+x^3) = 1 + 2*x^2 + x^3 + 12*x^4 + 12*x^5 + 35*x^6 + 48*x^7 + 280*x^8 + 516*x^9 + 1280*x^10 + 2368*x^11 + 6288*x^12 + 13216*x^13 + 29608*x^14 + 59836*x^15 + 178468*x^16 + 463300*x^17 + 1196199*x^18 +...

Mathematica

m = 34; A[_] = 1; Do[A[x_] = A[2x^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, 2*x^2+x^3)/(1-x +x*O(x^n))); polcoeff(A, n)}
for(n=0, 50, print1(a(n), ", "))

Crossrefs

Cf. A251572, A251581.

Sequence in context: A316194 A123773 A290433 * A328773 A330693 A329541

Adjacent sequences: A251579 A251580 A251581 * A251583 A251584 A251585

Keyword

nonn

Author

Paul D. Hanna, Jan 31 2015

Status

approved