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Search: id:A088795
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| A088795 |
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Fibonacci(n) as n runs through the quarter-squares. |
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1
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| 1, 2, 3, 5, 8, 13, 20, 30, 43, 60, 81, 107, 138, 175, 218, 268, 325, 390, 463, 545, 636, 737, 848, 970, 1103, 1248, 1405, 1575, 1758, 1955, 2166, 2392, 2633, 2890, 3163, 3453, 3760, 4085, 4428, 4790, 5171, 5572, 5993, 6435, 6898, 7383, 7890, 8420, 8973
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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This recurrence arose when a middle schooler was asked to complete a number sequence, given six of the Fibonacci numbers (1,2,3,5,8,13) but not told about the Fibonacci sequence.
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FORMULA
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a(n) = a(n-1) + 1 + A002620(n-2). For n<2: a(1)=1, a(2)=2. O.g.f.: x*(2*x^3-x^2-x+1)/((-1+x)^4*(x+1)). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 05 2007
a(n)=-1/16-3*n^2/8+17*n/12+n^3/12+(-1)^n/16. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 22 2009]
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EXAMPLE
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a(3) = a(2) + 1 + A002620(1) = 2+1+0 = 3
a(4) = a(3) + 1 + A002620(2) = 3+1+1 = 5
a(12) = a(11) + 1 + A002620(10) = 81+1+25 = 107.
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CROSSREFS
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Cf. A002620.
Sequence in context: A081612 A120761 A045842 this_sequence A156145 A059923 A055805
Adjacent sequences: A088792 A088793 A088794 this_sequence A088796 A088797 A088798
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KEYWORD
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nonn
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AUTHOR
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Stewart Charles Cureton (sarah.cureton(AT)att.net), Oct 16 2003
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