%I #12 Jun 12 2017 08:10:50
%S 3,49,322,1618,7119,28917,111360,412998,1490095,5266919,18329164,
%T 63032354,214788229,726753651,2445603148,8194841668,27369348241,
%U 91175639607,303133174298,1006289129240,3336552385073,11052905264953,36588907685926,121056347131508
%N Number of (undirected) paths in the grid graph P_3 X P_n.
%H Andrew Howroyd, <a href="/A288527/b288527.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 10*a(n-1)-37*a(n-2)+59*a(n-3)-27*a(n-4)-25*a(n-5)+21*a(n-6)+5*a(n-7)-4*a(n-8)-a(n-9) for n>9.
%F Empirical g.f.: x*(3 + 19*x - 57*x^2 + 34*x^3 + 43*x^4 - 7*x^5 - 13*x^6 - 2*x^7) / ((1 - x)^3*(1 - 2*x - x^2)^2*(1 - 3*x - x^2)). - _Colin Barker_, Jun 11 2017
%Y Row 3 of A288518.
%Y Cf. A288516.
%K nonn
%O 1,1
%A _Andrew Howroyd_, Jun 10 2017