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%I #21 Nov 09 2019 10:52:16
%S 1,3,5,11,19,34,62,107,191,335,587,1035,1812,3184,5589,9803,17213,
%T 30199,52999,93014,163214,286439,502655,882095,1547991,2716503,
%U 4767160,8365776,14680889,25763219,45211237,79340227,139232411,244335770,428779502,752455475
%N Sum of the products of pairs of Padovan numbers which are two apart, starting from A000931(5).
%F a(n) = Sum_{i=5..n+5} A000931(i)*A000931(i+2).
%F a(n) = A329227(n+7) - 1.
%F Conjectures from _Colin Barker_, Nov 09 2019: (Start)
%F G.f.: (1 + x - x^2 + x^3 - x^4) / ((1 - x)*(1 - 2*x + x^2 - x^3)*(1 + x - x^3)).
%F a(n) = 2*a(n-1) - 2*a(n-4) + 2*a(n-5) - 2*a(n-6) + a(n-7) for n>6.
%F (End)
%e For n=3, a(3) = 1*1 + 1*2 + 1*2 + 2*3 = 11.
%o (Python)
%o p = lambda x:[1, 1, 1][x] if x<3 else p(x-2)+p(x-3)
%o a = lambda x:sum(p(i)*p(i+2) for i in range(x+1))
%Y Cf. A000931, A133037, A329227.
%K nonn
%O 0,2
%A _David Nacin_, Nov 08 2019