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A054473 Number of ways of numbering the faces of a cube with nonnegative integers so that the sum of the 6 numbers is n. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

LINKS

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

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 *)

CROSSREFS

Cf. A039959.

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

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Last modified August 12 21:10 EDT 2020. Contains 336440 sequences. (Running on oeis4.)