A289864 - OEIS

%I #9 Jul 19 2017 10:14:38

%S 2,8,27,72,169,367,764,1553,3120,6234,12433,24790,49451,98705,197130,

%T 393879,787258,1573876,3146951,6292916,12584637,25167843,50333992,

%U 100665997,201329684,402656702,805310349,1610617218,3221230495,6442456549,12884908118,25769810675

%N Number of cliques in the n-triangular honeycomb queen graph.

%C Here, cliques means any complete subgraph (not just of maximum size).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Clique.html">Clique</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (5, -8, 2, 7, -7, 2).

%F a(n) = (4*n^3 - 18*n^2 - 68*n - 79 - (-1)^n + 3*2^(n + 5))/16.

%F a(n) = 5*a(n-10-8*a(n-2)+2*a(n-3)+7*a(n-4)-7*a(n-5)+2*a(n-6).

%F G.f.: (x*(-2 + 2*x - 3*x^2 + 3*x^3 + 5*x^4 - 2*x^5))/((-1 + x)^4*(-1 + x + 2*x^2)).

%t Table[(4 n^3 - 18 n^2 - 68 n - 79 - (-1)^n + 3 2^(n + 5))/16, {n, 20}]

%t LinearRecurrence[{5, -8, 2, 7, -7, 2}, {2, 8, 27, 72, 169, 367}, 20]

%t CoefficientList[Series[(-2 + 2 x - 3 x^2 + 3 x^3 + 5 x^4 - 2 x^5)/((-1 + x)^4 (-1 + x + 2 x^2)), {x, 0, 20}], x]

%K nonn,easy

%O 1,1

%A _Eric W. Weisstein_, Jul 13 2017