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A227374 G.f.: 1/(1 - x*(1-x^5)/(1 - x^2*(1-x^6)/(1 - x^3*(1-x^7)/(1 - x^4*(1-x^8)/(1 - x^5*(1-x^9)/(1 - ...)))))), a continued fraction. 7
1, 1, 1, 2, 3, 5, 8, 13, 22, 36, 61, 101, 169, 283, 473, 793, 1325, 2220, 3715, 6220, 10413, 17431, 29185, 48856, 81797, 136937, 229257, 383813, 642564, 1075762, 1800995, 3015171, 5047886, 8451001, 14148368, 23686705, 39655467, 66389797, 111147511, 186079299, 311527531, 521548600 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Limit a(n)/a(n+1) = 0.597312551712707899432116871133154503665320273329853...

LINKS

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

FORMULA

G.f.: T(0), where T(k) = 1 -  x^(k+1)*(1-x^(k+5))/(x^(k+1)*(1-x^(k+5)) - 1/T(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Oct 18 2013

EXAMPLE

G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 3*x^4 + 5*x^5 + 8*x^6 + 13*x^7 + 22*x^8 +...

MATHEMATICA

nMax = 42; 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]&; A227374 = col[4][[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+5))*CF+x*O(x^n))); polcoeff(CF, n)}

for(n=0, 50, print1(a(n), ", "))

CROSSREFS

Cf. A173173, A227360, A227375, A228644, A228645.

Column m=4 of A185646.

Sequence in context: A206743 A186085 A018151 * A124429 A306215 A018152

Adjacent sequences:  A227371 A227372 A227373 * A227375 A227376 A227377

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 09 2013

STATUS

approved

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Last modified April 8 02:27 EDT 2020. Contains 333312 sequences. (Running on oeis4.)