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URL: https://oeis.org/A388998

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A388998
Number of tetrahedra in the n X n queen graph.
0
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
Eric Weisstein's World of Mathematics, Graph Tetrahedron.
Eric Weisstein's World of Mathematics, Queen Graph.
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
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Dec 22 2025
STATUS
approved