A053719 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.

55, 70, 147, 226, 237, 275, 351, 409, 434, 610, 714, 717, 869, 934, 1085, 1369, 1490, 1602, 1643, 1954, 2363, 2405, 2534, 3020, 3241, 3450, 4017, 4039, 4060, 4140, 4796, 5766, 5830, 6412, 8601, 8635, 8855, 8885, 9423, 10083, 10224, 10809, 11115, 11935

Offset

0,1

Comments

j values are A053720 and k values are A053721

Links

Table of n, a(n) for n=0..43.

Example

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

Mathematica

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 *)

Crossrefs

Cf. A000330, A053720, A053721.

Sequence in context: A116055 A068898 A068899 * A217236 A050781 A060260

Adjacent sequences: A053716 A053717 A053718 * A053720 A053721 A053722

Keyword

easy,nice,nonn

Author

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

Extensions

Crossrefs in comments corrected by Jean-François Alcover, Oct 17 2012

Status

approved