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Search: id:A022109
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| A022109 |
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Fibonacci sequence beginning 1 19. |
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+0
3
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| 1, 19, 20, 39, 59, 98, 157, 255, 412, 667, 1079, 1746, 2825, 4571, 7396, 11967, 19363, 31330, 50693, 82023, 132716, 214739, 347455, 562194, 909649, 1471843, 2381492, 3853335, 6234827, 10088162, 16322989
(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(19;n-1-k,k),k=0..ceiling((n-1)/2)), n>=1, with a(-1)=18. These are the SW-NE diagonals in P(19;n,k), the (19,1) 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)=19. a(-1):=18.
G.f.: (1+18*x)/(1-x-x^2).
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MATHEMATICA
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a={}; b=1; c=19; 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(18, n+1) = A101220(18, 0, n+1).
Sequence in context: A007640 A054304 A151979 this_sequence A041730 A041732 A041728
Adjacent sequences: A022106 A022107 A022108 this_sequence A022110 A022111 A022112
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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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