Working on it and can get to some numbers in (1, 1) easily just following the pattern, but not everything. Example for c = 9253765:
( 1, 1, 2) {1:1:8:3:5:13} 65( 1, 1, 4) {1:1:32:7:25:41} 1025( 1, 1, 7) {1:1:98:13:85:113} 9605( 1, 1, 9) {1:1:162:17:145:181} 26245( 1, 1, 12) {1:1:288:23:265:313} 82945( 1, 1, 14) {1:1:392:27:365:421} 153665( 1, 1, 17) {1:1:578:33:545:613} 334085( 1, 1, 19) {1:1:722:37:685:761} 521285( 1, 1, 22) {1:1:968:43:925:1013} 937025( 1, 1, 24) {1:1:1152:47:1105:1201} 1327105( 1, 1, 27) {1:1:1458:53:1405:1513} 2125765( 1, 1, 29) {1:1:1682:57:1625:1741} 2829125( 1, 1, 32) {1:1:2048:63:1985:2113} 4194305( 1, 1, 34) {1:1:2312:67:2245:2381} 5345345( 1, 1, 37) {1:1:2738:73:2665:2813} 7496645( 1, 1, 39) {1:1:3042:77:2965:3121} 9253765
Also been rereading crumbs like mad and think these two are very relevant