A053678 - OEIS

%I #9 Dec 07 2012 05:03:38

%S 5,17,191,1412,2143,8393,5346,32475,99234,158712,393981,401023,514617,

%T 921485,577350,910495,1430793,3236406,462236,4122855

%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 k 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 k-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]; A053678 = Table[res = {i, j, k} /. ToRules[r[i]]; Print[res]; res, {i, A053676}][[All, 3]] (* _Jean-François Alcover_, Dec 07 2012 *)

%Y i values are A053676 and j values are A053677.

%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