Search: id:A022106
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%I A022106
%S A022106 1,16,17,33,50,83,133,216,349,565,914,1479,2393,3872,6265,
%T A022106 10137,16402,26539,42941,69480,112421,181901,294322,476223,
%U A022106 770545,1246768,2017313,3264081,5281394,8545475,13826869
%N A022106 Fibonacci sequence beginning 1 16.
%C A022106 a(n-1)=sum(P(16;n-1-k,k),k=0..ceiling((n-1)/2)), n>=1, with a(-1)=15. 
               These are the SW-NE diagonals in P(16;n,k), the (16,1) 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.
%H A022106 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%F A022106 a(n)= a(n-1)+a(n-2), n>=2, a(0)=1, a(1)=16. a(-1):=15.
%F A022106 G.f.: (1+15*x)/(1-x-x^2).
%t A022106 a={};b=1;c=16;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)
%Y A022106 a(n) = A109754(15, n+1) = A101220(15, 0, n+1).
%Y A022106 Sequence in context: A138599 A007636 A151977 this_sequence A041518 A042195 
               A041520
%Y A022106 Adjacent sequences: A022103 A022104 A022105 this_sequence A022107 A022108 
               A022109
%K A022106 nonn
%O A022106 0,2
%A A022106 N. J. A. Sloane (njas(AT)research.att.com).

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