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Search: id:A110036
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| A110036 |
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Constant terms of the partial quotients of the continued fraction expansion of 1 + Sum_{n>=0} 1/x^(2^n), where each partial quotient has the form {x + a(n)} after the initial constant term of 1. |
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3
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| 1, -1, 2, 0, 0, -2, 0, 2, 0, -2, 2, 0, -2, 0, 0, 2, 0, -2, 2, 0, 0, -2, 0, 2, -2, 0, 2, 0, -2, 0, 0, 2, 0, -2, 2, 0, 0, -2, 0, 2, 0, -2, 2, 0, -2, 0, 0, 2, -2, 0, 2, 0, 0, -2, 0, 2, -2, 0, 2, 0, -2, 0, 0, 2, 0, -2, 2, 0, 0, -2, 0, 2, 0, -2, 2, 0, -2, 0, 0, 2, 0, -2, 2, 0, 0, -2, 0, 2, -2, 0, 2, 0, -2, 0, 0, 2, -2, 0, 2, 0, 0, -2, 0, 2, 0, -2, 2, 0, -2, 0, 0, 2, -2, 0
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Suggested by Ralf Stephan.
For n>1, |a(n)| = 2*A090678(n) where A090678(n) = A088567(n) mod 2 and A088567(n) = number of "non-squashing" partitions of n into distinct parts.
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FORMULA
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G.f. (1-x+3*x^2+x^3)/(1+x^2) - 2*Sum_{k>=1} x^(3*2^(k-1))/Product_{j=0..k} (1+x^(2^j)).
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EXAMPLE
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1 + 1/x + 1/x^2 + 1/x^4 + 1/x^8 + 1/x^16 + ... =
[1; x - 1, x + 2, x, x, x - 2, x, x + 2, x, x - 2, ...].
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PROGRAM
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(PARI) contfrac(1+sum(n=0, 10, 1/x^(2^n)))
(PARI) {a(n)=polcoeff((1-x+3*x^2+x^3)/(1+x^2)- 2*sum(k=1, #binary(n), x^(3*2^(k-1))/prod(j=0, k, 1+x^(2^j)+x*O(x^n))), n)} (PARI) {a(n)=subst(contfrac(1+sum(k=0, #binary(n+1), 1/x^(2^k)))[n+1], x, 0)}
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CROSSREFS
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Cf. A090678, A088567.
Sequence in context: A025844 A035461 A029305 this_sequence A086937 A095759 A046113
Adjacent sequences: A110033 A110034 A110035 this_sequence A110037 A110038 A110039
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KEYWORD
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cofr,sign
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jul 08 2005
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