The set of forbidden pattern is {[1, 2, 3, 4], [1, 3, 2, 4], [1, 2, 4, 3]} This is the (RIGOROUS) scheme Warning, new definition for Chi [{[3, 4, 1, 2], [2, 3, 1, 4], [3, 4, 2, 1], [2, 1], [2, 4, 1, 3], [1, 2, 3], [1, 3, 2], [3, 1, 2]}, {[], [1], [1, 2], [2, 3, 1]}, table([ [1, 3, 2] = 2 [3, 4, 2, 1] = 3 [2, 4, 1, 3] = 1 [3, 1, 2] = 1 [1, 2, 3] = 3 [3, 4, 1, 2] = 1 [2, 1] = 1 [2, 3, 1, 4] = 4 ]), table([ [2, 3, 1] = {[3, 4, 1, 2], [2, 3, 1, 4], [3, 4, 2, 1], [2, 4, 1, 3]} [] = {[1]} [1, 2] = {[1, 2, 3], [1, 3, 2], [2, 3, 1]} [1] = {[2, 1], [1, 2]} ]), table([ [2, 3, 1] = {} [1, 3, 2] = {3} [3, 4, 2, 1] = {} [2, 4, 1, 3] = {4} [] = {} [1, 2] = {} [3, 1, 2] = {} [1, 2, 3] = {2, 3} [3, 4, 1, 2] = {} [2, 1] = {} [2, 3, 1, 4] = {3, 4} [1] = {} ])] This is the sequence [1, 1, 2, 6, 21, 80, 322, 1346, 5783, 25372, 113174, 511649, 2338988, 10793251, 50205607, 235156609, 1108120540, 5249646137, 24987770893, 119443412277, 573125649031, 2759515312908, 13328311926552, 64559295743113, 313530998739472, 1526333617345412, 7447070497787110, 36409703715788374, 178353171835771153, 875224495042876048, 4302111437028045585] This is the (Semi-Rigorous) Recurrence [1, 1, 2, 6, 21, 80, 322, 1346, 5783, 25372, 113174, 511649, 2338988, 10793251, 50205607, 235156609, 1108120540, 5249646137, 24987770893, 119443412277, 573125649031, 2759515312908, 13328311926552, 64559295743113, 313530998739472, 1526333617345412, 7447070497787110, 36409703715788374, 178353171835771153, 875224495042876048, 4302111437028045585]