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A053019 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.

%I A053019 #18 Sep 06 2023 22:41:53
%S A053019 46,142,290,1536,6126,894,6106,14539,9886,2020,21179,21502,13052,
%T A053019 15751,3830,42370,62580,6486,10150,56214,14984,21150,368668,354310,
%U A053019 558467,28810,38126,419690,1237147,49260,1056710,652670
%N A053019 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 A053019 i values are A053017 and j values are A053018.
%e A053019 Do(179) = 25665020 = 25236484 + 428536 = Do(178) + Do(46);
%e A053019 Do(184) = 27880600 = 15086400 + 12794200 = Do(150) + Do(142).
%t A053019 (* This is just a recomputation of k values, given i values. *)
%t A053019 A053017 = Cases[Import["https://oeis.org/A053017/b053017.txt", "Table"], {_, _}][[All, 2]];
%t A053019 do[n_] := n*(3*n - 1)*(3*n - 2)/2;
%t A053019 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 A053019 = triples[[All, 3]] (* _Jean-François Alcover_, Feb 17 2015, updated Jul 09 2022 *)
%K A053019 nice,nonn
%O A053019 1,1
%A A053019 Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Feb 24 2000
%E A053019 More terms from _Jon E. Schoenfield_, Aug 13 2007
%E A053019 a(27)-a(32) from _Donovan Johnson_, Aug 15 2010