A237655 G.f.: exp( Sum_{n>=1} 5*Fibonacci(n-2)*Fibonacci(n+2) * x^n/n ).

1, 10, 50, 175, 510, 1376, 3625, 9500, 24875, 65125, 170500, 446375, 1168625, 3059500, 8009875, 20970125, 54900500, 143731375, 376293625, 985149500, 2579154875, 6752315125, 17677790500, 46281056375, 121165378625, 317215079500, 830479859875, 2174224500125, 5692193640500, 14902356421375, 39014875623625

Offset: 0

Author

Paul D. Hanna, May 05 2014

Keywords

• nonn

Comments

Given g.f. A(x), note that A(x)^(1/5) is not an integer series.

Examples

			G.f.: A(x) = 1 + 10*x + 50*x^2 + 175*x^3 + 510*x^4 + 1376*x^5 + 3625*x^6 + ...
where the logarithm begins:
log(A(x)) = 5*1*2*x + 5*0*3*x^2/2 + 5*1*5*x^3/3 + 5*1*8*x^4/4 + 5*2*13*x^5/5 + 5*3*21*x^6/6 + 5*5*34*x^7/7 + 5*8*55*x^8/8 + 5*13*89*x^9/9 + ...
		

Links

• Fung Lam, Table of n, a(n) for n = 0..2000
• Index entries for linear recurrences with constant coefficients, signature (3, -1).

Crossrefs

Cf. A237654, A054888.

Programs

PARI

{a(n)=polcoeff(exp(sum(m=1, n, 5*fibonacci(m-2)*fibonacci(m+2) *x^m/m) +x*O(x^n)), n)}
for(n=0,30,print1(a(n),", "))

Formula

G.f.: (1+x)^7 / (1-3*x+x^2).

a(n) = 3*a(n-1) - a(n-2), n>=8. - Fung Lam, May 19 2014