Av(2413,3142,132), n=1..13: [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900]  Catalan: True
Av(2413,3142,213), n=1..13: [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900]  Catalan: True
Av(2413,3142,231), n=1..13: [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900]  Catalan: True
Av(2413,3142,312), n=1..13: [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900]  Catalan: True
Av(2413,3142,123), n=0..13: [1, 1, 2, 5, 12, 28, 65, 151, 351, 816, 1897, 4410, 10252, 23833]
   least-order recurrence fitting all 14 terms: a(n) = (3)*a(n-1) + (-2)*a(n-2) + (1)*a(n-3)
Av(2413,3142,321), n=0..13: [1, 1, 2, 5, 12, 28, 65, 151, 351, 816, 1897, 4410, 10252, 23833]
   least-order recurrence fitting all 14 terms: a(n) = (3)*a(n-1) + (-2)*a(n-2) + (1)*a(n-3)
ALL CHECKS PASSED
