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Search: id:A022110
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| A022110 |
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Fibonacci sequence beginning 1 20. |
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+0
3
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| 1, 20, 21, 41, 62, 103, 165, 268, 433, 701, 1134, 1835, 2969, 4804, 7773, 12577, 20350, 32927, 53277, 86204, 139481, 225685, 365166, 590851, 956017, 1546868, 2502885, 4049753, 6552638, 10602391
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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(20;n-1-k,k),k=0..ceiling((n-1)/2)), n>=1, with a(-1)=19. These are the SW-NE diagonals in P(20;n,k), the (20,1) 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)=20. a(-1):=19.
G.f.: (1+19*x)/(1-x-x^2).
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MATHEMATICA
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a={}; b=1; c=20; 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
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a(n) = A109754(19, n+1) = A101220(19, 0, n+1).
Sequence in context: A118865 A118608 A075034 this_sequence A041808 A041810 A042855
Adjacent sequences: A022107 A022108 A022109 this_sequence A022111 A022112 A022113
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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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