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A094707
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Partial sums of repeated Fibonacci sequence.
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2
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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; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Equals row sums of triangle A139147 starting with "1". - Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 11 2008
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (1,1,-1,1,-1).
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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(pi*n/2)+sqrt(4sqrt(5)/5-8/5)sin(pi*n/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);
a(n) = A131524(n)+A131524(n+1). - R. J. Mathar, Jul 07 2011
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CROSSREFS
| Cf. A000045.
Cf. A139147.
Sequence in context: A003412 A038348 A035945 * A117995 A033834 A127419
Adjacent sequences: A094704 A094705 A094706 * A094708 A094709 A094710
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), May 21 2004
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