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A101916
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G.f. satisfies: A(x) = 1/(1 + x*A(x^6)) and also the continued fraction: 1+x*A(x^7) = [1;1/x,1/x^6,1/x^36,1/x^216,...,1/x^(6^(n-1)),...].
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3
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1, -1, 1, -1, 1, -1, 1, 0, -1, 2, -3, 4, -5, 5, -4, 2, 1, -5, 10, -15, 19, -21, 20, -15, 5, 10, -29, 50, -70, 85, -90, 80, -51, 1, 69, -154, 244, -324, 375, -376, 307, -153, -91, 414, -788, 1163, -1469, 1621, -1529, 1115, -328, -833, 2299, -3916, 5440, -6550, 6874, -6039, 3741, 170, -5600, 12135, -18990, 25008
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,10
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COMMENTS
| Sequence A101916 is a look-a-like of the series expansion of B(x) = (1+x^6)/(1+x+x^6). The first difference occurs at a(43) = 415 versus a(43) = 414. [Johannes W. Meijer, Aug 08 2011]
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MAPLE
| nmax:=63: kmax:=nmax: for k from 0 to kmax do A:= proc(x): add(a(n)*x^n, n=0..k) end: f(x):=series(1/(1 + x*A(x^6)), x, k+1); for n from 0 to k do x(n):=coeff(f(x), x, n) od: a(k):=x(k): od: seq(a(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\6+1, A=1/(1+x*subst(A, x, x^6)+x*O(x^n))); polcoeff(A, n, x)} (PARI) {a(n)=local(M=contfracpnqn(concat(1, vector(ceil(log(n+1)/log(6))+1, n, 1/x^(6^(n-1)))))); polcoeff(M[1, 1]/M[2, 1]+x*O(x^(7*n+1)), 7*n+1)}
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CROSSREFS
| Cf. A101912-A101915, A101917-A101918.
Sequence in context: A200322 A075054 A158366 * A100771 A113771 A131845
Adjacent sequences: A101913 A101914 A101915 * A101917 A101918 A101919
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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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