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.

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

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-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+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