A391778 a(n) = n*(n-1)*(n- 2)^2*2^(n-4)/3.

0, 0, 1, 16, 120, 640, 2800, 10752, 37632, 122880, 380160, 1126400, 3221504, 8945664, 24227840, 64225280, 167116800, 427819008, 1079574528, 2689597440, 6624378880, 16148070400, 38997590016, 93381984256, 221878681600, 523449139200, 1226833920000, 2858032300032

Offset

1,4

Comments

Also the number of tetrahedra in the halved cube graph Q_n/2.

Links

Table of n, a(n) for n=1..28.

Eric Weisstein's World of Mathematics, Graph Tetrahedron.

Eric Weisstein's World of Mathematics, Halved Cube Graph.

Index entries for linear recurrences with constant coefficients, signature (10,-40,80,-80,32).

Formula

a(n) = 10*a(n-1)-40*a(n-2)+80*a(n-3)-80*a(n-4)+32*a(n-5).

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

Sum_{n>=3} 1/a(n) = Pi^2/2 + 3*log(2)*(1-log(2)) - 9/2. - Amiram Eldar, Jan 08 2026

Mathematica

Table[n (n - 1) (n - 2)^2 2^(n - 4)/3, {n, 28}]
LinearRecurrence[{10, -40, 80, -80, 32}, {0, 0, 1, 16, 120, 640}, 20]
CoefficientList[Series[x^2 (1 + 6 x)/(1 - 2 x)^5, {x, 0, 20}], x]

Crossrefs

Sequence in context: A374014 A014805 A022611 * A324066 A164542 A351383

Adjacent sequences: A391775 A391776 A391777 * A391779 A391780 A391781

Keyword

nonn,easy

Author

Eric W. Weisstein, Dec 19 2025

Status

approved