A295986 Number of maximal cliques in the n-halved cube graph.

1, 1, 1, 16, 56, 192, 624, 1920, 5632, 15872, 43264, 114688, 296960, 753664, 1880064, 4620288, 11206656, 26869760, 63766528, 149946368, 349700096, 809500672, 1861222400, 4253024256, 9663676416, 21843935232, 49140465664, 110058536960, 245484224512, 545460846592

Offset

1,4

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Halved Cube Graph

Eric Weisstein's World of Mathematics, Maximal Clique

Index entries for linear recurrences with constant coefficients, signature (8, -24, 32, -16).

Formula

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

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

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

Mathematica

Table[If[n < 4, 1, 2^(n - 4) (n^2 - 5 n + 12) (n + 2)/3], {n, 12}]
Join[{1, 1, 1}, LinearRecurrence[{8, -24, 32, -16}, {16, 56, 192, 624}, 30]]
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]

Prog

(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

Crossrefs

Sequence in context: A231971 A333279 A304692 * A169882 A202993 A221068

Adjacent sequences: A295983 A295984 A295985 * A295987 A295988 A295989

Keyword

nonn,easy

Author

Eric W. Weisstein, Dec 01 2017

Status

approved