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%I #10 Sep 02 2014 08:32:50
%S 1,1,4,11,47,172,725,2945,12592,53607,233115,1017428,4488097,19893325,
%T 88746008,397610355,1789394067,8081593288,36622787565,166442457597,
%U 758467464848,3464526761611,15859854880999,72747086739548,334290271569069,1538717057137809,7093579418490760
%N G.f.: 1 / AGM(1-5*x+x^2, 1+3*x+x^2).
%C Here AGM(x,y) = AGM((x+y)/2,sqrt(x*y)) is the arithmetic-geometric mean.
%H Vaclav Kotesovec, <a href="/A246652/b246652.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: 1 / AGM(1-x+x^2, sqrt((1-x+x^2)^2 - 16*x^2)).
%F 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
%F a(n) ~ (5+sqrt(21))^(n+1) / (Pi * n * 2^(n+3)). - _Vaclav Kotesovec_, Sep 02 2014
%e G.f.: A(x) = 1 + x + 4*x^2 + 11*x^3 + 47*x^4 + 172*x^5 + 725*x^6 +...
%o (PARI) {a(n)=polcoeff( 1 / agm(1-5*x+x^2, 1+3*x+x^2 +x*O(x^n)), n)}
%o for(n=0, 30, print1(a(n), ", "))
%o (PARI) {a(n)=polcoeff( 1 / agm(1-x+x^2, sqrt((1-x+x^2)^2 - 16*x^2 +x*O(x^n))), n)}
%o for(n=0, 30, print1(a(n), ", "))
%K nonn
%O 0,3
%A _Paul D. Hanna_, Aug 31 2014
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