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A099823
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G.f. is the continued fraction: A(x) = 1/[1 - x/[1 - (x-x^2)/[1 - (x^2-x^4)/[1 - (x^3-x^6)[1-... - (x^n-x^(2n))/[1 - ... ]]]]]]].
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1, 1, 2, 3, 5, 8, 12, 19, 29, 44, 67, 101, 153, 230, 346, 520, 780, 1171, 1755, 2631, 3942, 5905, 8846, 13247, 19839, 29707, 44482, 66604, 99722, 149309, 223546, 334692, 501096, 750226, 1123216, 1681635, 2517676, 3769356, 5643307, 8448900, 12649289
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| G.f.: A(x) = 1/(1-x*Sum_{n=0..inf} (-1)^n*[x^((3n+2)n) + x^((3n+1)(n+1))] ). a(n) = Sum_{k=0..m} (-1)^[n/2]*a(n-1-A001082(k)), where A001082(m)<n<=A001082(m+1).
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EXAMPLE
| A(x) = 1/(1 - x*(1 +x -x^5 -x^8 +x^16 +x^21 -x^33 -x^40 +x^56 +x^65 -x^85 -x^96 ++--... + (-1)^[n/2]*x^A001082(n) +...)).
a(n) = a(n-1) + a(n-2) - a(n-6) - a(n-9) + a(17) + a(n-22) --++...
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CROSSREFS
| Cf. A001082.
Sequence in context: A086676 A055804 A124062 * A023436 A024567 A060961
Adjacent sequences: A099820 A099821 A099822 * A099824 A099825 A099826
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Oct 26 2004
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