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A101918
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G.f. satisfies: A(x) = 1/(1 + x*A(x^8)) and also the continued fraction: 1+x*A(x^9) = [1;1/x,1/x^8,1/x^64,1/x^512,...,1/x^(8^(n-1)),...].
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7
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1, -1, 1, -1, 1, -1, 1, -1, 1, 0, -1, 2, -3, 4, -5, 6, -7, 7, -6, 4, -1, -3, 8, -14, 21, -28, 34, -38, 39, -36, 28, -14, -7, 35, -69, 107, -146, 182, -210, 224, -217, 182, -113, 6, 140, -322, 532, -756, 973, -1155, 1268, -1274, 1134, -812, 280, 476, -1449, 2604, -3872, 5146, -6280, 7092, -7372, 6896, -5447, 2843, 1029
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,12
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FORMULA
| G.f.: (1+x^8) / (1+x+x^8) (conjectured). - Ralf Stephan, May 17 2007
The conjecture is wrong. This G.f. produces a look-a-like of A101918. The first difference occurs at a(73) = -42106. The G.f. gives a(73) = -42105. [Johannes W. Meijer, Aug 08 2011]
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MAPLE
| nmax:=66: kmax:=nmax: for k from 0 to kmax do A:= proc(x): add(A101918(n)*x^n, n=0..k) end: f(x):=series(1/(1 + x*A(x^8)), x, k+1); for n from 0 to k do x(n):=coeff(f(x), x, n) od: A101918(k):=x(k): od: seq(A101918(n), n=0..nmax); # [Johannes W. Meijer, Aug 08 2011]
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PROG
| (PARI) {a(n)=local(A); A=1-x; for(i=1, n\8+1, A=1/(1+x*subst(A, x, x^8)+x*O(x^n))); polcoeff(A, n, x)} (PARI) {a(n)=local(M=contfracpnqn(concat(1, vector(ceil(log(n+1)/log(8))+1, n, 1/x^(8^(n-1)))))); polcoeff(M[1, 1]/M[2, 1]+x*O(x^(9*n+1)), 9*n+1)}
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CROSSREFS
| Cf. A101912-A101917.
Sequence in context: A066853 A141258 A117656 * A132125 A102672 A114955
Adjacent sequences: A101915 A101916 A101917 * A101919 A101920 A101921
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KEYWORD
| sign
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Dec 20 2004
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