A391978 a(n) = 2*n*binomial(n, 4).

0, 0, 0, 8, 50, 180, 490, 1120, 2268, 4200, 7260, 11880, 18590, 28028, 40950, 58240, 80920, 110160, 147288, 193800, 251370, 321860, 407330, 510048, 632500, 777400, 947700, 1146600, 1377558, 1644300, 1950830, 2301440, 2700720, 3153568, 3665200, 4241160, 4887330

Offset

1,4

Comments

Also the number of tetrahedra in the n X n rook graph.

Links

Table of n, a(n) for n=1..37.

Eric Weisstein's World of Mathematics, Graph Tetrahedron.

Eric Weisstein's World of Mathematics, Rook Graph.

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

a(n) = 2*A027764(n-1).

a(n) = (n-1)*(n-2)*(n-3)*n^2/12.

G.f.: 2*x^4*(4+x)/(-1+x)^6.

a(n) = 6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6).

From Amiram Eldar, Jan 08 2026: (Start)

Sum_{n>=4} 1/a(n) = 31/9 - Pi^2/3.

Sum_{n>=4} (-1)^n/a(n) = Pi^2/6 + 40*log(2)/3 - 97/9. (End)

Mathematica

Table[2 n Binomial[n, 4], {n, 40}]
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 0, 0, 8, 50, 180}, 40]
CoefficientList[Series[2 x^3 (4 + x)/(-1 + x)^6, {x, 0, 40}], x]

Crossrefs

Cf. A027764.

Sequence in context: A299686 A133426 A212063 * A300318 A290617 A163228

Adjacent sequences: A391975 A391976 A391977 * A391979 A391980 A391981

Keyword

nonn,easy

Author

Eric W. Weisstein, Dec 25 2025

Status

approved