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A227375 G.f.: 1/(1 - x*(1-x^6)/(1 - x^2*(1-x^7)/(1 - x^3*(1-x^8)/(1 - x^4*(1-x^9)/(1 - x^5*(1-x^10)/(1 - ...)))))), a continued fraction. 8
1, 1, 1, 2, 3, 5, 9, 14, 24, 41, 69, 118, 200, 340, 579, 985, 1677, 2854, 4858, 8270, 14078, 23966, 40798, 69453, 118235, 201280, 342655, 583328, 993046, 1690543, 2877949, 4899369, 8340598, 14198887, 24171937, 41149884, 70052848, 119256753, 203020631, 345618810, 588375486, 1001640259 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Radius of convergence r is a root of 1 - x - x^2 - x^3 + x^5 + x^6 + x^7 = 0,

where r = Limit a(n)/a(n+1) = 0.587411973105598587998520092901249815195963...

Compare to sequence A227376, generated by 1/(1-x-x^2-x^3+x^5+x^6+x^7).

LINKS

Table of n, a(n) for n=0..41.

FORMULA

Conjecture: G.f. -(x^4+x-1)*(x^5+x^4+x^3-x-1) / ( (x-1)*(x^4+x^3+x^2+x+1)*(x^7+x^6+x^5-x^3-x^2-x+1) ). - R. J. Mathar, Jul 17 2013

EXAMPLE

G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 3*x^4 + 5*x^5 + 9*x^6 + 14*x^7 + 24*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]&; A227375 = col[5][[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+6))*CF+x*O(x^n))); polcoeff(CF, n)

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

(PARI) /* From R. J. Mathar's g.f. formula: */

{a(n)=polcoeff((1-x-x^4)*(1+x-x^3-x^4-x^5)/((1-x^5)*(1-x-x^2-x^3+x^5+x^6+x^7) +x*O(x^n)), n)}

for(n=0, 50, print1(a(n), ", ")) \\ Paul D. Hanna, Jul 18 2013

CROSSREFS

Cf. A173173, A227374, A227360, A227376, A228644, A228645.

Column m=5 of A185646.

Sequence in context: A245800 A291896 A018155 * A032089 A105044 A026008

Adjacent sequences:  A227372 A227373 A227374 * A227376 A227377 A227378

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 09 2013

STATUS

approved

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Last modified April 9 20:55 EDT 2020. Contains 333363 sequences. (Running on oeis4.)