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

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).

Mathematica

Table[n (7 n^4 - 45 n^3 + 215 n^2 - 375 n + 183 - 15 (-1)^n)/60, {n, 20}]
LinearRecurrence[{4, -4, -4, 10, -4, -4, 4, -1}, {0, 1, 18, 68, 204, 501, 1106, 2208}, 20]
CoefficientList[Series[x (1 + 14 x + 8 x^3 + 19 x^4 + 14 x^5)/((-1 + x)^6 (1 + x)^2), {x, 0, 20}], x]

Crossrefs

Sequence in context: A063523 A045234 A158056 * A304061 A214491 A135470

Adjacent sequences: A388995 A388996 A388997 * A388999 A389000 A389001

Keyword

nonn,easy

Author

Eric W. Weisstein, Dec 22 2025

Status

approved