|
%I #19 Apr 28 2020 11:57:05
%S 2,16,81,471,1056,1381,6906,6906,17956,34531,40056,40056,200281,
%T 200281,200281,200281,520731,520731,1001406,1001406,1482081,1482081,
%U 1482081,1482081,7410406,7410406,7410406,7410406,7410406,7410406,7410406,7410406
%N Smallest number which is the sum of two positive triangular numbers (A000217) in at least n ways.
%H Donovan Johnson, <a href="/A234004/b234004.txt">Table of n, a(n) for n = 1..216</a>
%e 2 = 1+1; 16 = 1+15 = 6+10; 81 = 3+78 = 15+66 = 36+45.
%t poly[n_,k_]:=n (n-1)(k-2)/2+n;nn=10^5;order=3;t2=Table[0,{nn}];n2=Floor[(-4+#+Sqrt[(-4+#)^2+8 (-2+#) nn])/(2 (-2+#))&[order]];Do[r=Plus@@poly[{a,b},order];If[r<=nn,t2[[r]]++],{a,n2},{b,a,n2}];t={};n=1;While[a=Position[t2,_?(#>=n&),1,1];a!={},AppendTo[t,a[[1,1]]];n++];t (* after _T. D. Noe_ (A048610) *)
%Y Cf. A000217, A048610, A199809, A052346, A053587.
%K nonn
%O 1,1
%A _Vladimir Shevelev_ and _Peter J. C. Moses_, Dec 18 2013
|
