cp's OEIS Frontend

A220362 a(n) = Fibonacci(n-1) * Fibonacci(n) * Fibonacci(n+2).

%I A220362 #20 Apr 05 2016 00:31:22
%S A220362 0,3,10,48,195,840,3536,15015,63546,269280,1140535,4831632,20466720,
%T A220362 86699067,367262090,1555748880,6590255259,27916773720,118257343984,
%U A220362 500946159615,2122041966330,8989114051008,38078498128175,161303106631968,683290924545600
%N A220362 a(n) = Fibonacci(n-1) * Fibonacci(n) * Fibonacci(n+2).
%C A220362 An integral pentagon is a pentagon with integer sides and diagonals. There are two types of such pentagons.
%C A220362 Type B have sides A056570(n+2), A056570(n+2), A220363(n+2), A056570(n+2), A056570(n+2), and opposite diagonals a(n+2), A066258(n+2), A066258(n+2), A066258(n+2), a(n+2), for n=1,2,...
%D A220362 R. K. Guy, Unsolved Problems in Number Theory, D20.
%H A220362 Harvey P. Dale, <a href="/A220362/b220362.txt">Table of n, a(n) for n = 1..1000</a>
%H A220362 J. H. Jordan, B. E. Peterson, <a href="http://projecteuclid.org/euclid.rmjm/1181072619">Almost regular integer Fibonacci pentagons</a>, Rocky Mountain J. Math. Volume 23, Number 1 (1993), 243-247.
%F A220362 a(n) = 3*a(n-1) + 6*a(n-2) -3*a(n-3) - a(n-4); g.f.: (3x+x^2)/(1-3x-6x^2+3x^2+x^4) = x(3+x)/( (x^2-x-1)(x^2+4x-1) ). [_Ron Knott_, Jun 27 2013]
%F A220362 a(n) = 2*(-1)^n*Lucas(n-3)/25 + 3*(-1)^n*Lucas(n+1)/25 + Fibonacci(3*n+1)/5 = (1/5)*(-(-1)^n*Fibonacci(n-1) + 3*(-1)^n*Fibonacci(n) + Fibonacci(3*n+1)). - _Ehren Metcalfe_, Mar 26 2016
%t A220362 Table[Fibonacci[n - 1] * Fibonacci[n] * Fibonacci[n + 2], {n, 30}] (* _T. D. Noe_, Dec 13 2012 *)
%t A220362 #[[1]]*#[[2]]*#[[4]]&/@Partition[Fibonacci[Range[0,30]],4,1] (* _Harvey P. Dale_, Jan 16 2016 *)
%o A220362 (PARI) x='x+O('x^99); concat(0, Vec(x*(3+x)/((x^2-x-1)*(x^2+4*x-1)))) \\ _Altug Alkan_, Mar 26 2016
%K A220362 nonn
%O A220362 1,2
%A A220362 _Michel Marcus_, Dec 12 2012