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A022108
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Fibonacci sequence beginning 1 18.
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2
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1, 18, 19, 37, 56, 93, 149, 242, 391, 633, 1024, 1657, 2681, 4338, 7019, 11357, 18376, 29733, 48109, 77842, 125951, 203793, 329744, 533537, 863281, 1396818, 2260099, 3656917, 5917016, 9573933, 15490949
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n-1)=sum(P(18;n-1-k,k),k=0..ceiling((n-1)/2)), n>=1, with a(-1)=17. These are the SW-NE diagonals in P(18;n,k), the (18,1) 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
| Tanya Khovanova, Recursive Sequences
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FORMULA
| a(n)= a(n-1)+a(n-2), n>=2, a(0)=1, a(1)=18. a(-1):=17.
G.f.: (1+17*x)/(1-x-x^2).
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MATHEMATICA
| a={}; b=1; c=18; AppendTo[a, b]; AppendTo[a, c]; Do[b=b+c; AppendTo[a, b]; c=b+c; AppendTo[a, c], {n, 1, 12, 1}]; a (Vladimir Orlovsky, Jul 23 2008)
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CROSSREFS
| a(n) = A109754(17, n+1) = A101220(17, 0, n+1).
Sequence in context: A095393 A056022 A118510 * A041654 A041656 A042507
Adjacent sequences: A022105 A022106 A022107 * A022109 A022110 A022111
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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