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A022105 Fibonacci sequence beginning 1 15. +0
3
1, 15, 16, 31, 47, 78, 125, 203, 328, 531, 859, 1390, 2249, 3639, 5888, 9527, 15415, 24942, 40357, 65299, 105656, 170955, 276611, 447566, 724177, 1171743, 1895920, 3067663, 4963583, 8031246, 12994829 (list; graph; listen)
OFFSET

0,2

COMMENT

a(n-1)=sum(P(15;n-1-k,k),k=0..ceiling((n-1)/2)), n>=1, with a(-1)=14. These are the SW-NE diagonals in P(15;n,k), the (15,1) 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)=15. a(-1):=14.

G.f.: (1+14*x)/(1-x-x^2).

a(n) = A101220(14,0,n+1). - Ross La Haye (rlahaye(AT)new.rr.com), May 02 2006

MATHEMATICA

a={}; b=1; c=15; 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)

CROSSREFS

a(n) = A109754(14, n+1).

a(k) = A118654(4, k).

Sequence in context: A046417 A079832 A037971 this_sequence A041456 A041458 A041454

Adjacent sequences: A022102 A022103 A022104 this_sequence A022106 A022107 A022108

KEYWORD

nonn

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

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Last modified November 24 23:16 EST 2009. Contains 167481 sequences.


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