A054473 Number of ways of numbering the faces of a cube with nonnegative integers so that the sum of the 6 numbers is n.

1, 1, 3, 5, 10, 15, 29, 41, 68, 98, 147, 202, 291, 386, 528, 688, 906, 1151, 1480, 1841, 2310, 2833, 3484, 4207, 5099, 6076, 7259, 8562, 10104, 11796, 13785, 15948, 18462, 21201, 24339, 27747, 31633, 35827, 40572, 45695, 51436, 57618, 64520, 71918

Offset: 0

Author

Vladeta Jovovic, May 20 2000

Keywords

• easy
• nonn

Comments

Here we consider the symmetries of the cube in 3D space (mirror reflections are not allowed), see A097513. - Geoffrey Critzer, Sep 28 2013

Links

• Index entries for linear recurrences with constant coefficients, signature (1,2,0,-2,-4,1,3,3,1,-4,-2,0,2,1,-1).

Crossrefs

Cf. A039959, A097513.

Programs

Mathematica

nn=43;f[x_]=1/(1-x);CoefficientList[Series[1/24 (f[x]^6+6f[x]^2f[x^4]+3f[x]^2f[x^2]^2+8f[x^3]^2+6f[x^2]^3),{x,0,nn}],x] (* Geoffrey Critzer, Sep 28 2013 *)
LinearRecurrence[{1,2,0,-2,-4,1,3,3,1,-4,-2,0,2,1,-1},{1,1,3,5,10,15,29,41,68,98,147,202,291,386,528},50] (* Harvey P. Dale, Mar 05 2025 *)

Formula

G.f.: (3*x^6+x^5+x^4+1)/((1-x^4)*(1-x^3)^2*(1-x^2)^2*(1-x)).