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A101917
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G.f. satisfies: A(x) = 1/(1 + x*A(x^7)) and also the continued fraction: 1+x*A(x^8) = [1;1/x,1/x^7,1/x^49,1/x^343,...,1/x^(7^(n-1)),...].
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3
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1, -1, 1, -1, 1, -1, 1, -1, 2, -3, 4, -5, 6, -7, 8, -10, 13, -17, 22, -28, 35, -43, 53, -66, 83, -105, 133, -168, 211, -264, 330, -413, 518, -651, 819, -1030, 1294, -1624, 2037, -2555, 3206, -4025, 5055, -6349, 7973, -10010, 12565, -15771, 19796, -24851, 31200, -39173, 49183, -61748, 77519, -97315, 122166
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,9
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FORMULA
| G.f.: (1+x^7) / (1+x+x^7) (conjectured). - Ralf Stephan, May 17 2007
The conjecture is wrong. This G.f. produces a look-a-like of A101917. The first difference occurs at a(57) = - -153367. The G.f. gives a(57) = -153366. [Johannes W. Meijer, Aug 08 2011]
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MAPLE
| nmax:=57: kmax:=nmax: for k from 0 to kmax do A:= proc(x): add(A101917(n)*x^n, n=0..k) end: f(x):=series(1/(1 + x*A(x^7)), x, k+1); for n from 0 to k do x(n):=coeff(f(x), x, n) od: A101917(k):=x(k): od: seq(A101917(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\7+1, A=1/(1+x*subst(A, x, x^7)+x*O(x^n))); polcoeff(A, n, x)} (PARI) {a(n)=local(M=contfracpnqn(concat(1, vector(ceil(log(n+1)/log(7))+1, n, 1/x^(7^(n-1)))))); polcoeff(M[1, 1]/M[2, 1]+x*O(x^(8*n+1)), 8*n+1)}
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CROSSREFS
| Cf. A101912-A101916, A101918.
Sequence in context: A071218 A017901 A005709 * A127273 A143287 A033073
Adjacent sequences: A101914 A101915 A101916 * A101918 A101919 A101920
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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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