login
Number of induced paths in the n-ladder graph P_2 X P_n.
2

%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