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A388998

Number of tetrahedra in the n X n queen graph.

0, 1, 18, 68, 204, 501, 1106, 2208, 4104, 7153, 11858, 18804, 28756, 42581, 61362, 86304, 118864, 160641, 213522, 279556, 361116, 460757, 581394, 726144, 898520, 1102257, 1341522, 1620724, 1944740, 2318709, 2748274, 3239360, 3798432, 4432257, 5148178, 5953860

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Table of n, a(n) for n=1..36.

Eric Weisstein's World of Mathematics, Graph Tetrahedron.

Eric Weisstein's World of Mathematics, Queen Graph.

Index entries for linear recurrences with constant coefficients, signature (4,-4,-4,10,-4,-4,4,-1).

FORMULA

a(n) = n*(183-15*(-1)^n-375*n+215*n^2-45*n^3+7*n^4)/60.

G.f.: x^2*(1+14*x+8*x^3+19*x^4+14*x^5)/((-1+x)^6*(1+x)^2).

a(n) = 4*a(n-1)-4*a(n-2)-4*a(n-3)+10*a(n-4)-4*a(n-5)-4*a(n-6)+4*a(n-7)-a(n-8).