A053719 - OEIS

%I #7 Oct 17 2012 08:49:07

%S 55,70,147,226,237,275,351,409,434,610,714,717,869,934,1085,1369,1490,

%T 1602,1643,1954,2363,2405,2534,3020,3241,3450,4017,4039,4060,4140,

%U 4796,5766,5830,6412,8601,8635,8855,8885,9423,10083,10224,10809,11115,11935

%N Let Py(n)=A000330(n)=n-th square pyramidal number. Consider all integer triples (i,j,k), j >= k>0, with Py(i)=Py(j)+Py(k), ordered by increasing i; sequence gives i values.

%C j values are A053720 and k values are A053721

%e Py(55) = 56980 = Py(45) + Py(42); Py(70) = 116795 = Py(69) + Py(24);

%t r[i_, j_] := Reduce[ j >= k > 0 && (2i + 1)*(i + 1)*i == (2j + 1)*(j + 1)*j + (2k + 1)*(k + 1)*k, k, Integers]; ijk = Reap[ Do[ If[ r[i, j] =!= False, sol = {i, j, k} /. ToRules[r[i, j]]; Print[sol]; Sow[sol]], {i, 1, 12000}, {j, Floor[4i/5], i-1}]][[2, 1]]; A053719 = ijk[[All, 1]]; A053720 = ijk[[All, 2]]; A053721 = ijk[[All, 3]]; (* _Jean-François Alcover_, Oct 17 2012 *)

%Y Cf. A000330, A053720, A053721.

%K easy,nice,nonn

%O 0,1

%A Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Feb 11 2000

%E Crossrefs in comments corrected by _Jean-François Alcover_, Oct 17 2012