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A022102 Fibonacci sequence beginning 1 12. +0
3
1, 12, 13, 25, 38, 63, 101, 164, 265, 429, 694, 1123, 1817, 2940, 4757, 7697, 12454, 20151, 32605, 52756, 85361, 138117, 223478, 361595, 585073, 946668, 1531741, 2478409, 4010150, 6488559, 10498709 (list; graph; listen)
OFFSET

0,2

COMMENT

a(n-1)=sum(P(12;n-1-k,k),k=0..ceiling((n-1)/2)), n>=1, with a(-1)=11. These are the SW-NE diagonals in P(12;n,k), the (12,1) 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.

LINKS

Tanya Khovanova, Recursive Sequences

FORMULA

a(n)= a(n-1)+a(n-2), n>=2, a(0)=1, a(1)=12. a(-1):=11.

G.f.: (1+11*x)/(1-x-x^2).

CROSSREFS

a(n) = A109754(11, n+1) = A101220(11, 0, n+1).

Sequence in context: A108710 A108709 A138821 this_sequence A041292 A041679 A041294

Adjacent sequences: A022099 A022100 A022101 this_sequence A022103 A022104 A022105

KEYWORD

nonn

AUTHOR

njas

page 1

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Last modified July 8 18:40 EDT 2008. Contains 141013 sequences.


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