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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. 7
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified May 29 04:33 EDT 2020. Contains 334697 sequences. (Running on oeis4.)