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A277870 Ordered number of unit edges needed to build every 4-orthotope from hypercubes.

%I A277870 #20 Nov 07 2016 12:44:12
%S A277870 32,52,72,84,92,112,116,132,135,148,152,160,172,180,186,192,204,212,
%T A277870 216,232,237,244,248,252,256,260,272,276,288,292,297,308,312,316,326,
%U A277870 332,336,339,340,352,372,378,380,384,390,392,396,404,408,412,415,424,428
%N A277870 Ordered number of unit edges needed to build every 4-orthotope from hypercubes.
%C A277870 Ordered number of edges required to construct every hyperrectangle as a union of unit hypercubes. The sequence gives the n-th smallest such number, and generalizes the two-dimensional A047845 and the three-dimensional A090767 to four dimensions.
%C A277870 Does a(n) ~ n? - _Charles R Greathouse IV_, Nov 06 2016
%H A277870 Charles R Greathouse IV, <a href="/A277870/b277870.txt">Table of n, a(n) for n = 1..10000</a>
%H A277870 Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_polynomial">Symmetric polynomial</a>
%F A277870 These numbers are of the form: 4wxyz + 3(wxz+wyz+wxy+xyz) + 2(wx+wy+wz+xy+xz+yz) + w+x+y+z for any positive integers w, x, y, z.
%e A277870 a(1)=32 as this is the number of edges in the unit hypercube.
%t A277870 Edges[x_,y_,z_,w_]:=(4*x*y*z*w)+3*((w*x*z)+(w*y*z)+(w*x*y)+(x*y*z))+2*((w*x)+(w*y)+(w*z)+(x*y)+(x*z)+(y*z))+x+y+z+w;inputs=Tuples[Range[s],4];Union[Table[Edges[inputs[[k]][[1]],inputs[[k]][[2]],inputs[[k]][[3]],inputs[[k]][[4]]],{k,1,Length[inputs]}]]
%t A277870 Accuracy to 170 terms is achieved for s>=5764801, and for the entire list in the limit as s approaches infinity.
%o A277870 (PARI) list(lim)=my(v=List()); for(w=1,(lim-12)\20, for(x=1, min((lim-8*w-4)\(12*w+8),w), for(y=1,min((lim-5*w*x-3*x-3*w-1)\(7*w*x+5*x+5*w+3),x), forstep(n=((7*w+5)*y+(5*w+3))*x+(5*w + 3)*y+3*w+1, lim, ((4*w+3)*y+3*w+2)*x+(3*w+2)*y+2*w+1, listput(v,n))))); Set(v) \\ _Charles R Greathouse IV_, Nov 05 2016
%Y A277870 Cf. A047845, A090767.
%K A277870 nonn
%O A277870 1,1
%A A277870 _Eric R. Carter_, Nov 02 2016