A295986 - OEIS

%I #8 Dec 11 2017 05:06:59

%S 1,1,1,16,56,192,624,1920,5632,15872,43264,114688,296960,753664,

%T 1880064,4620288,11206656,26869760,63766528,149946368,349700096,

%U 809500672,1861222400,4253024256,9663676416,21843935232,49140465664,110058536960,245484224512,545460846592

%N Number of maximal cliques in the n-halved cube graph.

%H Colin Barker, <a href="/A295986/b295986.txt">Table of n, a(n) for n = 1..1000</a>

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

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

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8, -24, 32, -16).

%F a(n) = 2^(n - 4)*(n^2 - 5*n + 12)*(n + 2)/3 for n > 3.

%F a(n) = 8*a(n-1) - 24*a(n-2) + 32*a(n-3) - 16*a(n-4) for n > 7.

%F G.f.: x*(1 - 7*x + 17*x^2 - 64*x^4 + 112*x^5 - 64*x^6) / (1 - 2*x)^4. - _Colin Barker_, Dec 11 2017

%t Table[If[n < 4, 1, 2^(n - 4) (n^2 - 5 n + 12) (n + 2)/3], {n, 12}]

%t Join[{1, 1, 1}, LinearRecurrence[{8, -24, 32, -16}, {16, 56, 192, 624}, 30]]

%t CoefficientList[Series[(1 - 7 x + 17 x^2 - 64 x^4 + 112 x^5 - 64 x^6)/(-1 + 2 x)^4, {x, 0, 20}], x]

%o (PARI) Vec(x*(1 - 7*x + 17*x^2 - 64*x^4 + 112*x^5 - 64*x^6) / (1 - 2*x)^4 + O(x^40)) \\ _Colin Barker_, Dec 11 2017

%K nonn,easy

%O 1,4

%A _Eric W. Weisstein_, Dec 01 2017