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%I #50 Dec 07 2019 12:18:24
%S 1,2,8,55,610,10946,317811,14930352,1134903170,139583862445,
%T 27777890035288,8944394323791464,4660046610375530309,
%U 3928413764606871165730,5358359254990966640871840,11825896447871834976429068427,42230279526998466217810220532898
%N a(n) = Fibonacci(binomial(n+2,2)).
%C Diagonal of Fibonacci-Pascal triangle A045995.
%H Alois P. Heinz, <a href="/A081667/b081667.txt">Table of n, a(n) for n = 0..96</a>
%H Peter M. Chema, <a href="/A081667/a081667_1.pdf">Illustration of first 12 terms on a square spiral</a>
%H T. Kotek, J. A. Makowsky, <a href="http://arxiv.org/abs/1309.4020">Recurrence Relations for Graph Polynomials on Bi-iterative Families of Graphs</a>, arXiv preprint arXiv:1309.4020 [math.CO], 2013.
%F a(n) = sqrt(5)2^(-n(n+3)/2)(sqrt(5)+1)^((n^2+3n+2)/2)/10 + sqrt(5)2^(-n(n + 3)/2)(sqrt(5)-1)^((n^2+3n+ 2)/2)(-1)^(n(n+3)/2)/10.
%F a(n) = A045995(n+2,2).
%F a(n) = A000045(A000217(n+1)). - _Peter M. Chema_, Sep 18 2016. See the name.
%p with(combinat): seq(fibonacci((n^2-n)/2),n=2..16); # _Zerinvary Lajos_, May 18 2008
%p # second Maple program:
%p a:= n-> (<<0|1>, <1|1>>^((n+1)*(n+2)/2))[1, 2]:
%p seq(a(n), n=0..20); # _Alois P. Heinz_, Jan 20 2017
%t Table[Fibonacci[Binomial[n+2,2]],{n,0,20}] (* _Harvey P. Dale_, Dec 03 2014 *)
%o (Sage) [fibonacci(binomial(n,2)) for n in range(2, 17)] # _Zerinvary Lajos_, Nov 30 2009
%Y Cf. A000045, A000217, A033192, A045995, A054783.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Mar 26 2003
%E Name edited by _Michel Marcus_, Sep 25 2016
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