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

0,3

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).

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

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 *)

Prog

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

Crossrefs

Cf. A006008.

Row 3 of A327083.

Sequence in context: A283119 A091119 A243248 * A369421 A183721 A180797

Adjacent sequences: A046020 A046021 A046022 * A046024 A046025 A046026

Keyword

nonn,easy

Author

N. J. A. Sloane, Apr 11 2001

Status

approved