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 A094381 #5 Mar 30 2012 17:22:33 %S A094381 18,16,61,30,133,51,119,48,275,59,217,72,386,65,292,83,545,101,332,89, %T A094381 673,120,453,106,865,104 %N A094381 Number of numbers having exactly n representations as ab+ac+bc with 1 <= a <= b <= c. %C A094381 Numbers up to 250,000 were checked. Note that there seem to be many more numbers having an even number of representations. Note that the Mathematica program computes A094379, A094380 and A094381, but outputs only this sequence. %D A094381 See A025052 %e A094381 a(1) = 16 because there are 16 numbers (A093670) with unique representations. %t A094381 cntMax=10; nSol=Table[{0, 0, 0}, {cntMax+1}]; Do[lim=Ceiling[(n-1)/2]; cnt=0; Do[If[n>a*b && Mod[n-a*b, a+b]==0 && Quotient[n-a*b, a+b]>=b, cnt++; If[cnt>cntMax, Break[]]], {a, 1, lim}, {b, a, lim}]; If[cnt<=cntMax, If[nSol[[cnt+1, 1]]==0, nSol[[cnt+1, 1]]=n]; nSol[[cnt+1, 2]]=n; nSol[[cnt+1, 3]]++;], {n, 10000}]; Table[nSol[[i, 3]], {i, cntMax+1}] %Y A094381 Cf. A025052 (n having no representations), A093670 (n having one representation), A094379, A094380. %K A094381 nonn %O A094381 0,1 %A A094381 _T. D. Noe_, Apr 28 2004