A046023 Number of ways to color edges of a tetrahedron using <= n colors.

0, 1, 12, 87, 416, 1475, 4236, 10437, 22912, 45981, 85900, 151371, 254112, 409487, 637196, 962025, 1414656, 2032537, 2860812, 3953311, 5373600, 7196091, 9507212, 12406637, 16008576, 20443125, 25857676, 32418387, 40311712

Offset: 0

Author

N. J. A. Sloane, Apr 11 2001

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A006008.

Row 3 of A327083.

Programs

Maple

A046023 := n->(n^6+3*n^4+8*n^2)/12;

Mathematica

LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,1,12,87,416,1475,4236},30] (* Vincenzo Librandi, Jan 31 2012 *)

PARI

a(n)=(n^6+3*n^4+8*n^2)/12 \\ Charles R Greathouse IV, Jan 31 2012

Formula

a(n) = (n^6+3*n^4+8*n^2)/12.

G.f.: x*(1+x)*(1+4*x+20*x^2+4*x^3+x^4)/(1-x)^7. - Colin Barker, Jan 30 2012

E.g.f.: exp(x)*x*(12 + 60*x + 108*x^2 + 68*x^3 + 15*x^4 + x^5)/12. - Stefano Spezia, Feb 29 2024