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

0,4

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...

Links

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

Example

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 +...

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 *)

Prog

(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), ", "))

Crossrefs

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

Column m=2 of A185646.

Sequence in context: A050380 A241652 A241636 * A111077 A283189 A032157

Adjacent sequences: A227357 A227358 A227359 * A227361 A227362 A227363

Keyword

nonn

Author

Paul D. Hanna, Jul 08 2013

Status

approved