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Search: id:A022393
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| A022393 |
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Fibonacci sequence beginning 1 23. |
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+0
1
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| 1, 23, 24, 47, 71, 118, 189, 307, 496, 803, 1299, 2102, 3401, 5503, 8904, 14407, 23311, 37718, 61029, 98747, 159776, 258523, 418299, 676822, 1095121, 1771943, 2867064, 4639007, 7506071, 12145078
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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(23;n-1-k,k),k=0..ceiling((n-1)/2)), n>=1, with a(-1)=22. These are the SW-NE diagonals in P(23;n,k), the (23,1) 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)=23. a(-1):=22.
G.f.: (1+22*x)/(1-x-x^2).
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MATHEMATICA
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a={}; b=1; c=23; AppendTo[a, b]; AppendTo[a, c]; Do[b=b+c; AppendTo[a, b]; c=b+c; AppendTo[a, c], {n, 4!}]; a [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 18 2008]
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CROSSREFS
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Sequence in context: A007638 A031332 A122470 this_sequence A042068 A042066 A042070
Adjacent sequences: A022390 A022391 A022392 this_sequence A022394 A022395 A022396
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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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