%I A080097
%S A080097 0,3,8,24,63,168,440,1155,3024,7920,20735,54288,142128,372099,974168,
%T A080097 2550408,6677055,17480760,45765224,119814915,313679520,821223648,
%U A080097 2149991423,5628750624,14736260448,38580030723,101003831720
%N A080097 Fibonacci(n+2)^2 - 1.
%C A080097 a(n), a(n)+1 and a(n)+2 are consecutive members of A049997.
%F A080097 If n is odd, then a(n) = F(n+1)F(n+3) = F(n)F(n+4)-2, else a(n) = F(n)F(n+4) 
               = F(n+1)F(n+3)-2, where F(n) = Fibonacci numbers (A000045).
%F A080097 (1/5) {Lucas(2n+4) - 2(-1)^n - 5}.
%F A080097 G.f.: (3x+2x^2-x^3)/(1-x^2)(1-2x-2x^2+x^3)).
%t A080097 CoefficientList[Series[(3x+2x^2-x^3)/(1-x^2)(1-2x-2x^2+x^3)), {x, 0, 
               35}], x]
%Y A080097 Equals A007598(n+2) - 1. Cf. A064831, A059840.
%Y A080097 Sequence in context: A084920 A026556 A096001 this_sequence A096886 A056332 
               A091588
%Y A080097 Adjacent sequences: A080094 A080095 A080096 this_sequence A080098 A080099 
               A080100
%K A080097 easy,nonn
%O A080097 0,2
%A A080097 Mario Catalani (mario.catalani(AT)unito.it), Jan 29 2003
%E A080097 Edited by Ralf Stephan, May 15 2005