A141366 G.f.: A(x) = x - A(-A(x)^2).

1, 1, 2, 4, 8, 16, 32, 65, 138, 316, 792, 2142, 6052, 17316, 49160, 137108, 374632, 1004668, 2656872, 6974510, 18310220, 48416528, 129637152, 352339898, 971336204, 2707410220, 7596357720, 21363062480, 60019857952, 168132717792

Offset

1,3

Comments

What is Limit a(n+1)/a(n) = ? ; a(501)/a(500) = 2.91525180...

The limit is equal to 2.9240038... - Vaclav Kotesovec, Jan 06 2023

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..575

Formula

G.f.: A(x) = Series_Reversion( x + A(-x^2) ).

a(n) ~ c * d^n / n^(3/2), where d = 2.924003847... and c = 0.28352589... - Vaclav Kotesovec, Jan 06 2023

Example

G.f.: A(x) = x + x^2 + 2*x^3 + 4*x^4 + 8*x^5 + 16*x^6 + 32*x^7 + 65*x^8 +...
A(x)^2 = x^2 + 2*x^3 + 5*x^4 + 12*x^5 + 28*x^6 + 64*x^7 + 144*x^8 +...
Series_Reversion( A(x) ) = x + A(-x^2), thus:
x = A(x - x^2 + x^4 - 2*x^6 + 4*x^8 - 8*x^10 + 16*x^12 -+...).

Prog

(PARI) {a(n)=local(A=x+x^2); for(i=0, n, A=x-subst(A, x, -(A+x*O(x^n))^2)); polcoeff(A, n)}

Crossrefs

Sequence in context: A100137 A325917 A210542 * A049142 A367661 A303023

Adjacent sequences: A141363 A141364 A141365 * A141367 A141368 A141369

Keyword

nonn

Author

Paul D. Hanna, Jul 18 2008

Status

approved