%I #19 Dec 28 2024 22:16:08
%S 6,66,325,210,1596,2701,1326,903,1225,16836,6903,82621,141778,181503,
%T 63546,52975,354903,10440,13530,405450,7140,989121,1329265,511566,
%U 668746,437580,2102275,2001000,2469753,3229611,1428895,3096316,1963171,6843150,856086,4276350
%N a(n) = A185128(n) - A185129(n).
%D Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966, p. 197, no. 8.
%H N. J. A. Sloane, <a href="/A185128/a185128.jpg">Annotated scan of Beiler's Table 81</a>, based on page 197 of Beiler's "Recreations in the Theory of Numbers: The Queen of Mathematics Entertains", New York, Dover, First ed., 1964.
%t kmax=2000; TriangularQ[n_]:=IntegerQ[(Sqrt[1+8n]-1)/2]; A000217[n_]:=n(n+1)/2; a={}; For[k=1, k<=kmax, k++, For[h=1, A000217[h]<A000217[k], h++, If[TriangularQ[d=A000217[k] - A000217[h]] && TriangularQ[A000217[k]+A000217[h]], AppendTo[a,d]]]]; a (* _Stefano Spezia_, Sep 02 2024 *)
%o (PARI) lista(nn) = {v = vector(nn, n, n*(n+1)/2); for (n=2, nn, for (k=1, n-1, if (ispolygonal(v[n]+v[k], 3) && ispolygonal(v[n]-v[k], 3), print1(v[n]-v[k], ", "));););} \\ _Michel Marcus_, Jan 08 2015
%Y Cf. A000217, A185128, A185129, A185223, A185233, A185243, A185257, A185258.
%K nonn
%O 1,1
%A _Martin Renner_, Jan 20 2012
%E Edited by _N. J. A. Sloane_, Dec 28 2024 (replaced definition with simpler and more explicit formula from _Michel Marcus_, Jan 08 2015)