%I #9 Dec 28 2023 19:09:18
%S 1,8,25,58,117,218,387,666,1123,1868,3079,5044,8229,13388,21741,35262,
%T 57145,92558,149863,242590,392631,635408,1028235,1663848,2692297,
%U 4356368,7048897,11405506,18454653,29860418,48315339,78176034,126491659,204667988
%N Number of induced paths in the n-ladder graph P_2 X P_n.
%H Andrew Howroyd, <a href="/A360201/b360201.txt">Table of n, a(n) for n = 1..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LadderGraph.html">Ladder Graph</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-1,1)
%F a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + a(n-4) for n > 4.
%F G.f.: x*(1 + 5*x + 3*x^2)/((1 - x)^2*(1 - x - x^2)).
%t LinearRecurrence[{3,-2,-1,1},{1,8,25,58},40] (* _Harvey P. Dale_, Dec 28 2023 *)
%o (PARI) Vec((1 + 5*x + 3*x^2)/((1 - x)^2*(1 - x - x^2)) + O(x^40))
%Y Row 2 of A360199.
%K nonn,easy
%O 1,2
%A _Andrew Howroyd_, Jan 29 2023