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Search: id:A022392
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| A022392 |
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Fibonacci sequence beginning 1 22. |
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+0
1
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| 1, 22, 23, 45, 68, 113, 181, 294, 475, 769, 1244, 2013, 3257, 5270, 8527, 13797, 22324, 36121, 58445, 94566, 153011, 247577, 400588, 648165, 1048753, 1696918, 2745671, 4442589, 7188260, 11630849
(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(22;n-1-k,k),k=0..ceiling((n-1)/2)), n>=1, with a(-1)=21. These are the SW-NE diagonals in P(22;n,k), the (22,1) 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)=22. a(-1):=21.
G.f.: (1+21*x)/(1-x-x^2).
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MATHEMATICA
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a={}; b=1; c=22; 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: A106556 A106554 A118297 this_sequence A041976 A041978 A041980
Adjacent sequences: A022389 A022390 A022391 this_sequence A022393 A022394 A022395
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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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