id:A099823 - OEIS Search Results

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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; listen)

	OFFSET	`0,3`
	FORMULA	`G.f.: A(x) = 1/(1-xSum_{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).`
	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) --++...`
	CROSSREFS	`Cf. A001082.` `Sequence in context: A086676 A055804 A124062 this_sequence A023436 A024567 A060961` `Adjacent sequences: A099820 A099821 A099822 this_sequence A099824 A099825 A099826`
	KEYWORD	`nonn`
	AUTHOR	`Paul D. Hanna (pauldhanna(AT)juno.com), Oct 26 2004`

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Last modified December 10 12:37 EST 2009. Contains 170569 sequences.

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