id:A094707 - OEIS Search Results

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Partial sums of repeated Fibonacci sequence.

+0
3

0, 0, 1, 2, 3, 4, 6, 8, 11, 14, 19, 24, 32, 40, 53, 66, 87, 108, 142, 176, 231, 286, 375, 464, 608, 752, 985, 1218, 1595, 1972, 2582, 3192, 4179, 5166, 6763, 8360, 10944, 13528, 17709, 21890, 28655, 35420, 46366, 57312, 75023, 92734, 121391, 150048, 196416 (list; graph; listen)

	OFFSET	`0,4`
	COMMENT	`Equals row sums of triangle A139147 starting with "1". - Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 11 2008`
	FORMULA	`G.f. : x^2(1+x)/((1-x)(1-x^2-x^4)); a(n)=a(n-1)+a(n+2)-a(n-3)+a(n-4)-a(n-5); a(n)=sum{k=0..n, Fib(floor(k/2))}; a(n)=-2-(sqrt(5)/2-1/2)^(n/2)((2sqrt(5)/5-1)cos(pin/2)+sqrt(4sqrt(5)/5-8/5)sin(pin/2)) -(sqrt(5)/2+1/2)^(n/2)((sqrt(sqrt(5)/5+2/5)-sqrt(5)/5-1/2)(-1)^n-sqrt(sqrt(5)/5+2/5) -sqrt(5)/5-1/2);`
	CROSSREFS	`Cf. A000045.` `Cf. A139147.` `Sequence in context: A003412 A038348 A035945 this_sequence A117995 A033834 A127419` `Adjacent sequences: A094704 A094705 A094706 this_sequence A094708 A094709 A094710`
	KEYWORD	`easy,nonn`
	AUTHOR	`Paul Barry (pbarry(AT)wit.ie), May 21 2004`

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.

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