%I #18 Sep 06 2023 22:41:53

%S 46,142,290,1536,6126,894,6106,14539,9886,2020,21179,21502,13052,

%T 15751,3830,42370,62580,6486,10150,56214,14984,21150,368668,354310,

%U 558467,28810,38126,419690,1237147,49260,1056710,652670

%N Let Do(n) = A006566(n) = n-th dodecahedral number. Consider all integer triples (i,j,k), j >= k > 0, with Do(i) = Do(j) + Do(k), ordered by increasing i; sequence gives k values.

%C i values are A053017 and j values are A053018.

%e Do(179) = 25665020 = 25236484 + 428536 = Do(178) + Do(46);

%e Do(184) = 27880600 = 15086400 + 12794200 = Do(150) + Do(142).

%t (* This is just a recomputation of k values, given i values. *)

%t A053017 = Cases[Import["https://oeis.org/A053017/b053017.txt", "Table"], {_, _}][[All, 2]];

%t do[n_] := n*(3*n - 1)*(3*n - 2)/2;

%t triples = Reap[Module[{s, i, j, k, n, ijk}, s[i_] := Solve[j >= k > 0 && do[i] == do[j] + do[k], {j, k}, Integers]; For[n = 1, n <= Length[A053017], n++, i = A053017[[n]]; ijk = {i, j, k} /. s[i] // First; Print[ijk]; Sow[ijk]]]][[2, 1]];

%t A053019 = triples[[All, 3]] (* _Jean-François Alcover_, Feb 17 2015, updated Jul 09 2022 *)

%K nice,nonn

%O 1,1

%A Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Feb 24 2000

%E More terms from _Jon E. Schoenfield_, Aug 13 2007

%E a(27)-a(32) from _Donovan Johnson_, Aug 15 2010