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A081667 a(n) = Fibonacci(binomial(n+2,2)).

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