A227360 G.f.: 1/(1 - x*(1-x^3)/(1 - x^2*(1-x^4)/(1 - x^3*(1-x^5)/(1 - x^4*(1-x^6)/(1 - ...))))), a continued fraction.

1, 1, 1, 2, 2, 3, 5, 6, 10, 14, 21, 32, 46, 71, 104, 157, 235, 350, 527, 785, 1179, 1763, 2639, 3954, 5915, 8861, 13262, 19857, 29731, 44507, 66640, 99765, 149366, 223625, 334795, 501247, 750434, 1123518, 1682076, 2518314, 3770306, 5644701, 8450977, 12652376

Offset: 0

Author

Paul D. Hanna, Jul 08 2013

Keywords

• nonn

Comments

Compare to the continued fraction representation for the g.f. of A173173, where A173173(n) = ceiling(Fibonacci(n)/2).

Limit a(n)/a(n+1) = 0.6679357039724580760720733281356826861233293827578332775311...

Examples

			G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 2*x^4 + 3*x^5 + 5*x^6 + 6*x^7 + 10*x^8 +...
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A173173, A227374, A227375, A228644, A228645.

Column m=2 of A185646.

Programs

Mathematica

nMax = 44; col[m_ /; 0 <= m <= nMax] := 1/(1 + ContinuedFractionK[-x^k (1 - x^(m + k)), 1, {k, 1, Ceiling[nMax/2]}]) + O[x]^(2 nMax) // CoefficientList[#, x] &; A227360 = col[2][[1 ;; nMax]] (* Jean-François Alcover, Nov 03 2016 *)

PARI

{a(n)=local(CF); CF=1+x; for(k=0, n, CF=1/(1 - x^(n-k+1)*(1 - x^(n-k+3))*CF+x*O(x^n))); polcoeff(CF, n)}
for(n=0,50,print1(a(n),", "))