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Search: id:A022107
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| A022107 |
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Fibonacci sequence beginning 1 17. |
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+0
3
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| 1, 17, 18, 35, 53, 88, 141, 229, 370, 599, 969, 1568, 2537, 4105, 6642, 10747, 17389, 28136, 45525, 73661, 119186, 192847, 312033, 504880, 816913, 1321793, 2138706, 3460499, 5599205, 9059704, 14658909
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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(17;n-1-k,k),k=0..ceiling((n-1)/2)), n>=1, with a(-1)=16. These are the SW-NE diagonals in P(17;n,k), the (17,1) 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)=17. a(-1):=16.
G.f.: (1+16*x)/(1-x-x^2).
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CROSSREFS
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a(n) = A109754(16, n+1) = A101220(16, 0, n+1).
Adjacent sequences: A022104 A022105 A022106 this_sequence A022108 A022109 A022110
Sequence in context: A098159 A018821 A111054 this_sequence A041584 A041586 A041588
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KEYWORD
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nonn
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AUTHOR
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njas
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