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%I #9 Dec 07 2012 05:03:30
%S 6,40,454,2600,2586,20175,48103,93097,105805,265195,755100,803007,
%T 1211000,1111974,1493421,1499160,2622000,4309280,5127195,5574139
%N Let Oc(n) = A005900(n) = n-th octahedral number. Consider all integer triples (i,j,k), j >= k > 0, with Oc(i) = Oc(j)+Oc(k), ordered by increasing i; sequence gives j values.
%e Oc(7) = 231 = Oc(6) + Oc(5); Oc(41) = 45961 = Oc(40) + Oc(17); Oc(465) = 67029905 = Oc(454) + Oc(191)
%t (* This is just a check of j-values, given i-values *) A053676 = {7, 41, 465, 2732, 3005, 20648, 48125, 94396, 129299, 282931, 789281, 835050, 1241217, 1292143, 1521647, 1603655, 2756953, 4847702, 5128447, 6242598}; r[i_] := Reduce[0 < k <= j && 2*i^3 + i == 2*j^3 + j + 2*k^3 + k, {j, k}, Integers]; A053677 = Table[res = {i, j, k} /. ToRules[r[i]]; Print[res]; res, {i, A053676}][[All, 2]] (* _Jean-François Alcover_, Dec 07 2012 *)
%Y i values are A053676 and k values are A053678.
%K nice,nonn
%O 1,1
%A Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Feb 16 2000
%E More terms from Larry Reeves (larryr(AT)acm.org), May 07 2001
%E a(13)-a(16) from _Donovan Johnson_, Jun 21 2010
%E a(17)-a(20) from _Donovan Johnson_, Sep 29 2010