A277308 G.f. satisfies: A(x - 3*A(x)^2) = x - A(x)^2.

1, 2, 20, 298, 5492, 116124, 2710776, 68308170, 1831522940, 51744512380, 1529687560328, 47075470016012, 1502258036769256, 49560341916549320, 1686236991420431760, 59054595629732284890, 2125432920387784135812, 78509698415432235272292, 2972996232264052816975752, 115303660044380692013332428

Offset

1,2

Links

Paul D. Hanna, Table of n, a(n) for n = 1..300

Formula

G.f. A(x) also satisfies:

(1) A(x) = x + 2 * A( 3*A(x)/2 - x/2 )^2.

(2) A(x) = x/3 + 2/3 * Series_Reversion(x - 3*A(x)^2).

(3) R(x) = 3*x - 2 * Series_Reversion(x - A(x)^2), where R(A(x)) = x.

(4) R( sqrt( x/2 - R(x)/2 ) ) = 3*x/2 - R(x)/2, where R(A(x)) = x.

a(n) = Sum_{k=0..n-1} A277295(n,k) * 3^k * 2^(n-k-1).

Example

G.f.: A(x) = x + 2*x^2 + 20*x^3 + 298*x^4 + 5492*x^5 + 116124*x^6 + 2710776*x^7 + 68308170*x^8 + 1831522940*x^9 + 51744512380*x^10 +...

Prog

(PARI) {a(n) = my(A=[1], F=x); for(i=1, n, A=concat(A, 0); F=x*Ser(A); A[#A] = -polcoeff(subst(F, x, x-3*F^2) + F^2, #A) ); A[n]}
for(n=1, 30, print1(a(n), ", "))

Crossrefs

Cf. A277295, A213591, A275765, A276360, A276361, A276362, A276363.

Cf. A277300, A277301, A277302, A277303, A277304, A277305, A277306, A277307, A277309.

Cf. A276364.

Sequence in context: A349963 A246482 A124211 * A128481 A367862 A177397

Adjacent sequences: A277305 A277306 A277307 * A277309 A277310 A277311

Keyword

nonn

Author

Paul D. Hanna, Oct 09 2016

Status

approved