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Search: id:A022104
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| A022104 |
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Fibonacci sequence beginning 1 14. |
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+0
4
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| 1, 14, 15, 29, 44, 73, 117, 190, 307, 497, 804, 1301, 2105, 3406, 5511, 8917, 14428, 23345, 37773, 61118, 98891, 160009, 258900, 418909, 677809, 1096718, 1774527, 2871245, 4645772, 7517017, 12162789
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n-1)=sum(P(14;n-1-k,k),k=0..ceiling((n-1)/2)), n>=1, with a(-1)=13. These are the SW-NE diagonals in P(14;n,k), the (14,1) Pascal triangle. Cf. A093645 for the (10,1) Pascal triangle. Observation by Paul Barry (pbarry(AT)wit.ie, Apr 29 2004. Proof via recursion relations and comparison of inputs.
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LINKS
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Tanya Khovanova, Recursive Sequences
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FORMULA
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a(n)= a(n-1)+a(n-2), n>=2, a(0)=1, a(1)=14. a(-1):=13.
G.f.: (1+13*x)/(1-x-x^2).
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MATHEMATICA
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a={}; b=1; c=14; AppendTo[a, b]; AppendTo[a, c]; Do[b=b+c; AppendTo[a, b]; c=b+c; AppendTo[a, c], {n, 1, 9, 1}]; a (Vladimir Orlovsky, Jul 22 2008)
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CROSSREFS
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a(n) = A109754(13, n+1) = A101220(13, 0, n+1).
Sequence in context: A087430 A085900 A075659 this_sequence A041398 A041919 A041400
Adjacent sequences: A022101 A022102 A022103 this_sequence A022105 A022106 A022107
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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