This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A054473 #18 Mar 07 2025 13:01:51
%S A054473 1,1,3,5,10,15,29,41,68,98,147,202,291,386,528,688,906,1151,1480,1841,
%T A054473 2310,2833,3484,4207,5099,6076,7259,8562,10104,11796,13785,15948,
%U A054473 18462,21201,24339,27747,31633,35827,40572,45695,51436,57618,64520,71918
%N A054473 Number of ways of numbering the faces of a cube with nonnegative integers so that the sum of the 6 numbers is n.
%C A054473 Here we consider the symmetries of the cube in 3D space (mirror reflections are not allowed), see A097513. - _Geoffrey Critzer_, Sep 28 2013
%H A054473 <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,0,-2,-4,1,3,3,1,-4,-2,0,2,1,-1).
%F A054473 G.f.: (3*x^6+x^5+x^4+1)/((1-x^4)*(1-x^3)^2*(1-x^2)^2*(1-x)).
%t A054473 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 *)
%t A054473 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 *)
%Y A054473 Cf. A039959, A097513.
%K A054473 easy,nonn
%O A054473 0,3
%A A054473 _Vladeta Jovovic_, May 20 2000