A207829 First line of square array such that T[n+1,k] = | T[n,k] +/- T[n,k+1] |, filling antidiagonals with the smallest possible positive integers not occuring earlier.

1, 2, 4, 7, 8, 10, 13, 12, 16, 20, 19, 32, 24, 34, 29, 40, 31, 45, 52, 42, 62, 81, 46, 47, 91, 68, 111, 70, 84, 99, 61, 113, 80, 78, 125, 85, 141, 105, 102, 130, 55, 106, 142, 168, 98, 188, 135, 120, 189, 150

A208054 T(n,k)=Number of nXk nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any horizontal, vertical or antidiagonal neighbor (colorings ignoring permutations of colors)

1, 1, 1, 2, 2, 2, 5, 15, 15, 5, 15, 203, 716, 203, 15, 52, 4140, 83440, 83440, 4140, 52, 203, 115975, 18171918, 112073062, 18171918, 115975, 203, 877, 4213597, 6423127757, 346212384169, 346212384169, 6423127757, 4213597, 877, 4140, 190899322

A208053 Number of nX5 nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any horizontal, vertical or antidiagonal neighbor (colorings ignoring permutations of colors)

15, 4140, 18171918, 346212384169, 18633407199331522

A208052 Number of nX4 nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any horizontal, vertical or antidiagonal neighbor (colorings ignoring permutations of colors)

5, 203, 83440, 112073062, 346212384169, 2043836452962923, 20538493062072286871, 324446721789278481458200, 7600607444778834885508561198, 252518539060608935260165703671351

A208051 Number of nX3 nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any horizontal, vertical or antidiagonal neighbor (colorings ignoring permutations of colors)

2, 15, 716, 83440, 18171918, 6423127757, 3376465219485, 2486327138729353, 2454996141671330713, 3143641561804718358884, 5084413934903476204054959, 10166624612435356414640715276, 24691194409056203926713355839051

A208050 T(n,k)=Number of nXk 0..3 arrays with new values 0..3 introduced in row major order and no element equal to any horizontal, vertical or antidiagonal neighbor (colorings ignoring permutations of colors)

1, 1, 1, 2, 2, 2, 5, 8, 8, 5, 14, 32, 44, 32, 14, 41, 128, 244, 244, 128, 41, 122, 512, 1356, 1904, 1356, 512, 122, 365, 2048, 7540, 14976, 14976, 7540, 2048, 365, 1094, 8192, 41932, 118096, 168096, 118096, 41932, 8192, 1094, 3281, 32768, 233204, 931968

A208049 Number of nX7 0..3 arrays with new values 0..3 introduced in row major order and no element equal to any horizontal, vertical or antidiagonal neighbor (colorings ignoring permutations of colors)

122, 2048, 41932, 931968, 21472544, 502504448, 11838995200, 279733684992, 6617787903744, 156641740131072, 3708483510235904, 87806041737925888, 2079067090247547648, 49228778299543155968, 1165660962446546688768

A208048 Number of nX6 0..3 arrays with new values 0..3 introduced in row major order and no element equal to any horizontal, vertical or antidiagonal neighbor (colorings ignoring permutations of colors)

41, 512, 7540, 118096, 1897888, 30818432, 502504448, 8206614784, 134107752704, 2192020679040, 35832132655104, 585752326535168, 9575474013944320, 156533905282970624, 2558923378953086464, 41831786939400151040

A208047 Number of nX5 0..3 arrays with new values 0..3 introduced in row major order and no element equal to any horizontal, vertical or antidiagonal neighbor (colorings ignoring permutations of colors)

14, 128, 1356, 14976, 168096, 1897888, 21472544, 243113056, 2753187616, 31181409632, 353155643424, 3999817236576, 45301793546528, 513087070702432, 5811214258319904, 65817707844947552, 745450199930022688

A208046 Number of nX4 0..3 arrays with new values 0..3 introduced in row major order and no element equal to any horizontal, vertical or antidiagonal neighbor (colorings ignoring permutations of colors)

5, 32, 244, 1904, 14976, 118096, 931968, 7356288, 58068800, 458389760, 3618506752, 28564366592, 225486229504, 1779981604864, 14051122574336, 110919150841856, 875592537571328, 6911901929525248, 54562352063938560, 430713614487224320