A275131 -id:A275131 - cp's OEIS frontend

A275129 Number of nX6 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,0) or (-1,1) and new values introduced in order 0..2.

122, 1024, 2607, 11092, 71576, 473185, 3146574, 20970214, 139845553, 930732169, 6190918966, 41214051338, 274484938098, 1827596183195, 12167228578454, 81014307245606, 539449424460354, 3591778777900364, 23914435700214624

Offset: 1

R. H. Hardin, Jul 17 2016

nonn

Column 6 of A275131.

			Some solutions for n=4
..0..0..0..1..1..1. .0..0..1..1..1..2. .0..0..1..2..1..2. .0..0..0..1..1..2
..1..1..2..0..2..0. .2..2..0..0..0..1. .1..2..0..0..0..1. .1..1..2..2..0..1
..2..0..1..1..1..2. .0..1..2..1..2..0. .0..1..2..2..2..0. .0..0..1..1..2..2
..1..2..0..0..0..1. .2..0..0..0..1..2. .2..0..0..1..1..1. .2..2..0..0..1..0

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 67

Cf. A275131.

Empirical recurrence of order 67 (see link above)

A275126 Number of n X 3 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,0) or (-1,1) and new values introduced in order 0..2.

Original entry on oeis.org

5, 16, 45, 129, 373, 1083, 3148, 9157, 26623, 77372, 224857, 653525, 1899462, 5520787, 16046124, 46637722, 135551305, 393976458, 1145083415, 3328158969, 9673218248, 28114986916, 81715561920, 237504397813, 690301064559

Offset: 1

R. H. Hardin, Jul 17 2016

nonn

			Some solutions for n=4:
..0..1..2. .0..0..0. .0..0..0. .0..1..0. .0..0..0. .0..0..1. .0..1..1
..2..0..1. .1..1..2. .1..1..1. .2..2..2. .1..1..1. .2..2..0. .2..2..0
..1..2..2. .2..0..1. .2..2..2. .0..1..1. .2..0..2. .0..1..1. .1..1..1
..0..1..0. .1..2..0. .1..1..0. .2..0..0. .1..1..0. .2..0..0. .0..2..0

R. H. Hardin, Table of n, a(n) for n = 1..210

Column 3 of A275131.

Empirical: a(n) = 3*a(n-1) - 2*a(n-2) + 4*a(n-3) + a(n-4) + 3*a(n-5) + 8*a(n-6) + a(n-7) - 3*a(n-8) - a(n-9) for n>10.

Empirical g.f.: x*(5 + x + 7*x^2 + 6*x^3 + 7*x^4 + 11*x^5 - 4*x^6 - 10*x^7 - 5*x^8 - x^9) / (1 - 3*x + 2*x^2 - 4*x^3 - x^4 - 3*x^5 - 8*x^6 - x^7 + 3*x^8 + x^9). - Colin Barker, Jan 31 2019

A275127 Number of nX4 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,0) or (-1,1) and new values introduced in order 0..2.

Original entry on oeis.org

14, 64, 174, 568, 2178, 8321, 31772, 121707, 466252, 1783920, 6825273, 26122839, 99981686, 382636173, 1464403303, 5604594713, 21449747744, 82091326930, 314176968483, 1202409074708, 4601819411125, 17611921823170, 67403757335393

Offset: 1

R. H. Hardin, Jul 17 2016

nonn

Column 4 of A275131.

			Some solutions for n=4
..0..1..1..2. .0..1..1..2. .0..0..0..1. .0..0..1..1. .0..0..0..1
..2..0..0..1. .2..0..0..0. .1..1..2..2. .1..2..2..0. .2..1..2..2
..1..2..2..2. .1..1..1..2. .2..0..1..1. .0..1..1..1. .0..0..1..1
..0..1..0..1. .2..2..0..1. .1..2..0..0. .2..0..2..0. .2..2..0..0

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A275131.

Empirical: a(n) = 5*a(n-1) -9*a(n-2) +19*a(n-3) -9*a(n-4) -9*a(n-5) +87*a(n-6) -46*a(n-7) -84*a(n-8) +7*a(n-9) -59*a(n-10) -45*a(n-11) +31*a(n-12) +23*a(n-13) +4*a(n-14) -a(n-15) -a(n-16) +a(n-17) for n>20

A275128 Number of nX5 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,0) or (-1,1) and new values introduced in order 0..2.

Original entry on oeis.org

41, 256, 675, 2545, 12423, 62378, 315021, 1591442, 8024937, 40445177, 203778488, 1026594464, 5172646773, 26068048495, 131374129725, 662045442417, 3336258461916, 16812605674569, 84724677500065, 426956397683686

Offset: 1

R. H. Hardin, Jul 17 2016

nonn

Column 5 of A275131.

			Some solutions for n=4
..0..1..0..2..1. .0..1..1..2..2. .0..0..1..1..2. .0..0..0..1..1
..2..2..1..0..0. .2..0..0..1..1. .2..2..0..0..0. .1..1..2..2..0
..0..0..2..2..2. .1..2..2..0..0. .0..1..1..2..2. .0..0..1..1..2
..2..1..1..1..0. .0..1..1..2..2. .2..0..0..1..1. .2..2..0..0..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A275131.

Empirical: a(n) = 8*a(n-1) -27*a(n-2) +79*a(n-3) -99*a(n-4) -81*a(n-5) +860*a(n-6) -1162*a(n-7) -868*a(n-8) +1676*a(n-9) -3352*a(n-10) -1549*a(n-11) +4857*a(n-12) +1164*a(n-13) +3213*a(n-14) +5946*a(n-15) -1377*a(n-16) -5652*a(n-17) -4880*a(n-18) -2760*a(n-19) -710*a(n-20) +595*a(n-21) +1142*a(n-22) +594*a(n-23) +71*a(n-24) +48*a(n-25) +20*a(n-26) +a(n-28) for n>31

A275130 Number of nX7 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,0) or (-1,1) and new values introduced in order 0..2.

Original entry on oeis.org

365, 4096, 10077, 48451, 412306, 3586068, 31446544, 276145917, 2432426709, 21443562178, 188954647355, 1664477862236, 14666416028009, 129260090882281, 1139083482681178, 10037066997078506, 88448338430227606, 779467930298530878

Offset: 1

R. H. Hardin, Jul 17 2016

nonn

Column 7 of A275131.

			Some solutions for n=4
..0..0..1..1..2..2..0. .0..1..1..1..2..2..0. .0..1..1..2..2..0..0
..2..2..0..0..0..1..1. .2..2..2..0..1..1..1. .2..0..0..1..1..1..2
..1..1..2..2..2..2..0. .0..1..1..2..2..2..0. .1..1..2..0..2..0..0
..2..0..0..1..1..1..2. .2..2..0..1..0..1..2. .2..0..1..1..1..2..2

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A275131.

A275132 Number of 3 X n 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,0) or (-1,1) and new values introduced in order 0..2.

Original entry on oeis.org

2, 12, 45, 174, 675, 2607, 10077, 38967, 150651, 582435, 2251827, 8706015, 33659139, 130132935, 503119779, 1945160703, 7520376939, 29075268471, 112410752211, 434602254687, 1680258482619, 6496212425799, 25115645192451, 97102063806447

Offset: 1

R. H. Hardin, Jul 17 2016

nonn

			Some solutions for n=4:
..0..1..1..2. .0..0..0..1. .0..1..0..1. .0..1..1..1. .0..1..1..1
..2..2..0..0. .1..1..2..0. .2..2..2..2. .2..2..0..0. .2..2..0..0
..1..1..1..2. .0..0..1..1. .0..1..1..0. .0..1..2..2. .0..1..1..2

R. H. Hardin, Table of n, a(n) for n = 1..210

Row 3 of A275131.

Empirical: a(n) = 3*a(n-1) + 2*a(n-2) + 6*a(n-3) - 2*a(n-4) - 4*a(n-5) for n>6.

Empirical g.f.: x*(2 + 6*x + 5*x^2 + 3*x^3 - 5*x^4 - 4*x^5) / ((1 + x + 2*x^2)*(1 - 4*x + 2*x^3)). - Colin Barker, Jan 31 2019

A275133 Number of 4 X n 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,0) or (-1,1) and new values introduced in order 0..2.

Original entry on oeis.org

4, 36, 129, 568, 2545, 11092, 48451, 212897, 933888, 4092697, 17946318, 78700481, 345078541, 1513083403, 6634687537, 29092060534, 127563508661, 559344843153, 2452635533674, 10754397617406, 47156241405767, 206772290181505

Offset: 1

R. H. Hardin, Jul 17 2016

nonn

			Some solutions for n=4:
..0..0..1..1. .0..0..1..1. .0..0..1..2. .0..0..1..0. .0..0..0..1
..2..2..0..0. .2..2..0..0. .1..2..0..0. .2..2..2..2. .1..1..2..0
..1..1..1..2. .0..1..2..2. .0..1..1..1. .0..0..1..1. .0..0..1..2
..0..0..0..1. .2..0..0..0. .2..2..0..0. .2..2..0..0. .2..2..0..0

R. H. Hardin, Table of n, a(n) for n = 1..210

Row 4 of A275131.

Empirical: a(n) = a(n-1) + 8*a(n-2) + 22*a(n-3) + 36*a(n-4) + 7*a(n-5) - 48*a(n-6) - 4*a(n-7) + 15*a(n-8) - 18*a(n-9) for n>11.

Empirical g.f.: x*(4 + 32*x + 61*x^2 + 63*x^3 + 9*x^4 - 159*x^5 - 201*x^6 + 113*x^7 + 39*x^8 - 104*x^9 + 48*x^10) / (1 - x - 8*x^2 - 22*x^3 - 36*x^4 - 7*x^5 + 48*x^6 + 4*x^7 - 15*x^8 + 18*x^9). - Colin Barker, Jan 31 2019

A275134 Number of 5Xn 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,0) or (-1,1) and new values introduced in order 0..2.

Original entry on oeis.org

8, 108, 373, 2178, 12423, 71576, 412306, 2381629, 13727957, 79158451, 456572944, 2633093481, 15185124732, 87573269532, 505049273961, 2912660248825, 16797581275481, 96873339396362, 558678129749247, 3221951115220504

Offset: 1

R. H. Hardin, Jul 17 2016

nonn

Row 5 of A275131.

			Some solutions for n=4
..0..1..0..1. .0..1..2..1. .0..1..0..2. .0..0..1..1. .0..1..0..0
..2..2..2..0. .2..0..0..0. .2..2..1..1. .1..2..2..0. .2..2..1..1
..1..1..1..2. .1..1..2..2. .0..0..2..0. .0..1..1..2. .0..0..2..2
..2..2..0..1. .0..0..0..1. .2..1..1..1. .2..2..0..1. .1..1..0..0
..1..1..2..2. .1..1..2..0. .0..2..2..2. .0..1..2..2. .2..2..2..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A275131.

Empirical: a(n) = a(n-1) +16*a(n-2) +49*a(n-3) +109*a(n-4) +31*a(n-5) -508*a(n-6) +75*a(n-7) +324*a(n-8) -972*a(n-9) +260*a(n-10) for n>14

A275135 Number of 6Xn 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,0) or (-1,1) and new values introduced in order 0..2.

Original entry on oeis.org

16, 324, 1083, 8321, 62378, 473185, 3586068, 27224209, 206864716, 1571281413, 11942779144, 90722922402, 689405748706, 5238174766697, 39801761785044, 302425691696718, 2297924356585952, 17460451254284279, 132669830674540739

Offset: 1

R. H. Hardin, Jul 17 2016

nonn

Row 6 of A275131.

			Some solutions for n=4
..0..1..0..1. .0..0..1..2. .0..0..0..0. .0..0..1..0. .0..1..1..1
..2..2..2..0. .2..2..0..0. .1..2..1..1. .2..2..2..2. .2..2..0..0
..1..1..1..2. .1..1..2..1. .0..0..2..2. .1..0..1..1. .0..1..1..2
..0..0..0..0. .2..0..0..0. .1..1..0..0. .2..2..0..0. .2..2..0..1
..1..1..2..2. .1..1..2..2. .2..2..2..2. .1..1..2..2. .0..1..2..2
..0..0..1..1. .0..0..0..1. .0..1..0..0. .0..0..1..1. .2..0..0..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A275131.

Empirical: a(n) = a(n-1) +32*a(n-2) +117*a(n-3) +301*a(n-4) -196*a(n-5) -6255*a(n-6) -3361*a(n-7) -3603*a(n-8) -22745*a(n-9) +165021*a(n-10) +8504*a(n-11) -100758*a(n-12) +692296*a(n-13) -1045155*a(n-14) -356088*a(n-15) +1094300*a(n-16) -3137949*a(n-17) +2346676*a(n-18) +3048039*a(n-19) -3364817*a(n-20) +4783757*a(n-21) +1001864*a(n-22) -4054644*a(n-23) +818224*a(n-24) -774400*a(n-26) for n>28

A275136 Number of 7 X n 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,0) or (-1,1) and new values introduced in order 0..2.

Original entry on oeis.org

32, 972, 3148, 31772, 315021, 3146574, 31446544, 315531602, 3172042022, 31863778966, 320131530703, 3216908659843, 32328900869180, 324884120562167, 3264789400925918, 32809744239367085, 329717318770636840

Offset: 1

R. H. Hardin, Jul 17 2016

nonn

Row 7 of A275131.

			Some solutions for n=4
..0..1..0..0. .0..0..1..0. .0..0..0..0. .0..1..0..2. .0..1..0..0
..2..2..1..1. .2..2..2..2. .1..1..1..1. .2..2..1..0. .2..2..1..1
..1..0..2..2. .1..1..1..1. .0..2..2..2. .1..0..2..2. .1..0..2..2
..2..1..1..1. .2..2..0..0. .1..0..0..0. .2..1..1..0. .2..1..0..0
..0..2..0..2. .0..1..2..2. .2..1..1..1. .0..2..2..2. .0..2..2..2
..1..1..1..0. .2..0..0..1. .0..2..2..2. .1..0..1..0. .1..0..0..0
..0..0..2..1. .1..2..2..0. .1..0..1..0. .2..2..2..1. .2..2..1..1

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 53

Cf. A275131.

Empirical recurrence of order 53 (see link above).

cp's OEIS Frontend

A275129 Number of nX6 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,0) or (-1,1) and new values introduced in order 0..2.

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A275126 Number of n X 3 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,0) or (-1,1) and new values introduced in order 0..2.

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A275127 Number of nX4 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,0) or (-1,1) and new values introduced in order 0..2.

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A275128 Number of nX5 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,0) or (-1,1) and new values introduced in order 0..2.

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A275130 Number of nX7 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,0) or (-1,1) and new values introduced in order 0..2.

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A275132 Number of 3 X n 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,0) or (-1,1) and new values introduced in order 0..2.

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A275133 Number of 4 X n 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,0) or (-1,1) and new values introduced in order 0..2.

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A275134 Number of 5Xn 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,0) or (-1,1) and new values introduced in order 0..2.

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A275135 Number of 6Xn 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,0) or (-1,1) and new values introduced in order 0..2.

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A275136 Number of 7 X n 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,0) or (-1,1) and new values introduced in order 0..2.

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