A246652 G.f.: 1 / AGM(1-5*x+x^2, 1+3*x+x^2).

1, 1, 4, 11, 47, 172, 725, 2945, 12592, 53607, 233115, 1017428, 4488097, 19893325, 88746008, 397610355, 1789394067, 8081593288, 36622787565, 166442457597, 758467464848, 3464526761611, 15859854880999, 72747086739548, 334290271569069, 1538717057137809, 7093579418490760

Offset

0,3

Comments

Here AGM(x,y) = AGM((x+y)/2,sqrt(x*y)) is the arithmetic-geometric mean.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Formula

G.f.: 1 / AGM(1-x+x^2, sqrt((1-x+x^2)^2 - 16*x^2)).

Recurrence: (n-3)*n^2*a(n) = (n-3)*(3*n^2 - 3*n + 1)*a(n-1) + (n-1)*(10*n^2 - 40*n + 31)*a(n-2) - (n-2)*(9*n^2 - 36*n + 29)*a(n-3) + (n-3)*(10*n^2 - 40*n + 31)*a(n-4) + (n-1)*(3*n^2 - 21*n + 37)*a(n-5) - (n-4)^2*(n-1)*a(n-6). - Vaclav Kotesovec, Sep 02 2014

a(n) ~ (5+sqrt(21))^(n+1) / (Pi * n * 2^(n+3)). - Vaclav Kotesovec, Sep 02 2014

Example

G.f.: A(x) = 1 + x + 4*x^2 + 11*x^3 + 47*x^4 + 172*x^5 + 725*x^6 +...

Prog

(PARI) {a(n)=polcoeff( 1 / agm(1-5*x+x^2, 1+3*x+x^2 +x*O(x^n)), n)}
for(n=0, 30, print1(a(n), ", "))
(PARI) {a(n)=polcoeff( 1 / agm(1-x+x^2, sqrt((1-x+x^2)^2 - 16*x^2 +x*O(x^n))), n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Sequence in context: A149302 A149303 A053882 * A254202 A149304 A149305

Adjacent sequences: A246649 A246650 A246651 * A246653 A246654 A246655

Keyword

nonn

Author

Paul D. Hanna, Aug 31 2014

Status

approved