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

0,3

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

Table of n, a(n) for n=0..43.

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

Formula

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

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 *)

Crossrefs

Cf. A039959, A097513.

Sequence in context: A008337 A077285 A072523 * A265508 A327042 A006168

Adjacent sequences: A054470 A054471 A054472 * A054474 A054475 A054476

Keyword

easy,nonn

Author

Vladeta Jovovic, May 20 2000

Status

approved