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
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).
Programs
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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)).
Comments