A340893 G.f. A(x) satisfies: A(x) = (1 - x*A(x)) * Sum_{n>=0} x^n / (1 - x*A(x)^(2*n+1)).

1, 1, 1, 3, 12, 51, 229, 1079, 5288, 26768, 139255, 741804, 4035428, 22374787, 126262588, 724423620, 4222889705, 24999907277, 150274982778, 917156371139, 5684147494421, 35782117189675, 228878225147773, 1488242327844714, 9842110656790201

Offset

0,4

Links

Table of n, a(n) for n=0..24.

Formula

G.f. A(x) satisfies:

(1) A(x) = (1 - x*A(x)) * Sum_{n>=0} x^n / (1 - x*A(x)^(2*n+1)).

(2) A(x) = (1 - x*A(x)) * Sum_{n>=0} x^n*A(x)^n / (1 - x*A(x)^(2*n)).

Example

G.f.: A(x) = 1 + x + x^2 + 3*x^3 + 12*x^4 + 51*x^5 + 229*x^6 + 1079*x^7 + 5288*x^8 + 26768*x^9 + 139255*x^10 + 741804*x^11 + 4035428*x^12 + ...
where
A(x)/(1 - x*A(x)) = 1/(1 - x*A(x)) + x/(1 - x*A(x)^3) + x^2/(1 - x*A(x)^5) + x^3/(1 - x*A(x)^7) + x^4/(1 - x*A(x)^9) + ...
also
A(x)/(1 - x*A(x)) = 1/(1-x) + x*A(x)/(1 - x*A(x)^2) + x^2*A(x)^2/(1 - x*A(x)^4) + x^3*A(x)^3/(1 - x*A(x)^6) + x^4*A(x)^4/(1 - x*A(x)^8) + ...

Prog

(PARI) {a(n) = my(A=1); for(i=1, n, A = (1-x*A) * sum(m=0, n, x^m / (1 - x*A^(2*m+1) +x*O(x^n)) ) ); polcoeff(H=A, n)}
for(n=0, 30, print1(a(n), ", "))
(PARI) {a(n) = my(A=1); for(i=1, n, A = (1-x*A) * sum(m=0, n, x^m*A^m / (1 - x*A^(2*m) +x*O(x^n)) ) ); polcoeff(H=A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A340361, A340891, A340892.

Sequence in context: A151185 A151186 A151187 * A151188 A151189 A199875

Adjacent sequences: A340890 A340891 A340892 * A340894 A340895 A340896

Keyword

nonn

Author

Paul D. Hanna, Jan 25 2021

Status

approved