A275401 -id:A275401 - cp's OEIS frontend

A275395 Number of n X 2 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,0) or (-1,1) and new values introduced in order 0..2.

2, 9, 16, 31, 63, 129, 260, 534, 1083, 2210, 4496, 9157, 18653, 37980, 77372, 157551, 320905, 653525, 1331010, 2710764, 5520787, 11243865, 22899407, 46637722, 94983335, 193445757, 393976458, 802382692, 1634153628, 3328158969, 6778215744

Offset: 1

R. H. Hardin, Jul 26 2016

nonn

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

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

Column 2 of A275401.

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

Empirical g.f.: x*(2 + 5*x - 4*x^2 - 4*x^3 + 10*x^4 + 3*x^5 - 14*x^6 + 4*x^7 - 2*x^8 + 2*x^9) / (1 - 2*x - x^2 + 3*x^3 - x^4 - 4*x^5 + 3*x^6 - x^7 + 2*x^8 - x^9). - Colin Barker, Feb 04 2019

A275396 Number of nX3 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,0) or (-1,1) and new values introduced in order 0..2.

Original entry on oeis.org

5, 54, 84, 178, 394, 1017, 2645, 6980, 18464, 48959, 129079, 340418, 895555, 2359728, 6219251, 16402499, 43261910, 114071354, 300754298, 792805040, 2090067487, 5510137826, 14527552687, 38302379482, 100983905166, 266240696535

Offset: 1

R. H. Hardin, Jul 26 2016

nonn

Column 3 of A275401.

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

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

Cf. A275401.

Empirical: a(n) = 3*a(n-1) +4*a(n-2) -19*a(n-3) +a(n-4) +65*a(n-5) -47*a(n-6) -99*a(n-7) +83*a(n-8) +66*a(n-9) -4*a(n-10) -60*a(n-11) -73*a(n-12) +36*a(n-13) +121*a(n-14) -88*a(n-15) +13*a(n-16) +8*a(n-17) -19*a(n-18) +20*a(n-19) -7*a(n-20) -a(n-21) +2*a(n-22) -a(n-23) +a(n-24) for n>28

A275397 Number of nX4 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,0) or (-1,1) and new values introduced in order 0..2.

Original entry on oeis.org

14, 324, 444, 1011, 2404, 8122, 27373, 94065, 323306, 1109170, 3808690, 13056118, 44831206, 154016128, 529240302, 1819237762, 6248275627, 21463735564, 73700124392, 253141996437, 869508060107, 2987025162013, 10261553235393

Offset: 1

R. H. Hardin, Jul 26 2016

nonn

Column 4 of A275401.

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

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

Cf. A275401.

Empirical: a(n) = 8*a(n-1) -8*a(n-2) -103*a(n-3) +300*a(n-4) +490*a(n-5) -3088*a(n-6) +729*a(n-7) +15630*a(n-8) -17249*a(n-9) -43708*a(n-10) +76246*a(n-11) +72849*a(n-12) -154108*a(n-13) -140650*a(n-14) +150868*a(n-15) +459072*a(n-16) -68123*a(n-17) -1257353*a(n-18) +287606*a(n-19) +1776435*a(n-20) +89259*a(n-21) -3152687*a(n-22) +1585958*a(n-23) +2120249*a(n-24) -5693936*a(n-25) +8738939*a(n-26) -2087559*a(n-27) -14377928*a(n-28) +19318593*a(n-29) -4920957*a(n-30) -10078471*a(n-31) +14579538*a(n-32) -11939970*a(n-33) +3348781*a(n-34) +6751098*a(n-35) -9831957*a(n-36) +5660046*a(n-37) -420212*a(n-38) -1779949*a(n-39) +989592*a(n-40) -102542*a(n-41) +603187*a(n-42) -1100852*a(n-43) +634094*a(n-44) +123594*a(n-45) -502838*a(n-46) +404369*a(n-47) -101943*a(n-48) -68068*a(n-49) +76892*a(n-50) -37448*a(n-51) +7233*a(n-52) +7592*a(n-53) -6103*a(n-54) +4317*a(n-55) -1620*a(n-56) -31*a(n-57) +504*a(n-58) -240*a(n-59) -9*a(n-60) +56*a(n-61) -51*a(n-62) +19*a(n-63) -7*a(n-64) +a(n-65) for n>69

A275398 Number of n X 5 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,0) or (-1,1) and new values introduced in order 0..2.

Original entry on oeis.org

41, 1944, 2344, 5758, 14884, 65045, 283169, 1266905, 5656712, 25396322, 114023115, 510915912, 2291881500, 10263922489, 46052282280, 206639693889, 927930559927, 4167565838387, 18709473097471, 83993025347677, 376914801778863

Offset: 1

R. H. Hardin, Jul 26 2016

nonn

Column 5 of A275401.

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

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

Cf. A275401.

A275399 Number of nX6 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,0) or (-1,1) and new values introduced in order 0..2.

Original entry on oeis.org

122, 11664, 12376, 32771, 91849, 518049, 2940064, 17159883, 100110527, 587134035, 3434767901, 20106677263, 117757352942, 690470416676, 4056447811022, 23833910585917, 140089258343730, 822721587908577, 4830773713211697

Offset: 1

R. H. Hardin, Jul 26 2016

nonn

Column 6 of A275401.

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

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

Cf. A275401.

A275400 Number of nX7 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,0) or (-1,1) and new values introduced in order 0..2.

Original entry on oeis.org

365, 69984, 65344, 186538, 566331, 4142271, 30551417, 232200615, 1766745035, 13518543301, 103511190946, 793366592691, 6084436180732, 46693188566604, 358610775107181, 2756060353163818, 21192914770286797, 163023210361243535

Offset: 1

R. H. Hardin, Jul 26 2016

nonn

Column 7 of A275401.

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

R. H. Hardin, Table of n, a(n) for n = 1..195

Cf. A275401.

A275402 Number of 3 X n 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,0) or (-1,1) and new values introduced in order 0..2.

Original entry on oeis.org

3, 16, 84, 444, 2344, 12376, 65344, 345008, 1821600, 9617824, 50780928, 268117056, 1415625088, 7474326400, 39463524352, 208362556160, 1100128676352, 5808544139776, 30668398841856, 161925374911488, 854946069256192

Offset: 1

R. H. Hardin, Jul 26 2016

nonn

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

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

Row 3 of A275401.

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

Empirical g.f.: x*(3 + 4*x + 2*x^2) / (1 - 4*x - 6*x^2 - 4*x^3). - Colin Barker, Feb 04 2019

A275403 Number of 4_X_n 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,0) or (-1,1) and new values introduced in order 0..2.

Original entry on oeis.org

6, 31, 178, 1011, 5758, 32771, 186538, 1061795, 6043830, 34402035, 195819682, 1114623859, 6344543534, 36113737251, 205562777626, 1170082606339, 6660219918630, 37910596295955, 215790669012498, 1228300722808403

Offset: 1

R. H. Hardin, Jul 26 2016

nonn

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

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

Row 4 of A275401.

Empirical: a(n) = 3*a(n-1) + 11*a(n-2) + 25*a(n-3) + 2*a(n-4) - 24*a(n-5) for n>6.

Empirical g.f.: x*(6 + 13*x + 19*x^2 - 14*x^3 - 20*x^4 + 8*x^5) / (1 - 3*x - 11*x^2 - 25*x^3 - 2*x^4 + 24*x^5). - Colin Barker, Feb 04 2019

A275404 Number of 5 X n 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,0) or (-1,1) and new values introduced in order 0..2.

Original entry on oeis.org

12, 63, 394, 2404, 14884, 91849, 566331, 3495079, 21564220, 133044851, 820883765, 5064781430, 31249159768, 192804508189, 1189585924729, 7339632833601, 45284849272769, 279403286034674, 1723892118671285, 10636253097506243

Offset: 1

R. H. Hardin, Jul 26 2016

nonn

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

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

Row 5 of A275401.

Empirical: a(n) = 2*a(n-1) + 15*a(n-2) + 55*a(n-3) + 69*a(n-4) + 8*a(n-5) - 50*a(n-6) + 14*a(n-7) + a(n-8) - a(n-9) for n>10.

Empirical g.f.: x*(12 + 39*x + 88*x^2 + 11*x^3 - 127*x^4 - 92*x^5 + 63*x^6 + 16*x^7 - 20*x^8 + x^9) / (1 - 2*x - 15*x^2 - 55*x^3 - 69*x^4 - 8*x^5 + 50*x^6 - 14*x^7 - x^8 + x^9). - Colin Barker, Feb 04 2019

A275405 Number of 6Xn 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,0) or (-1,1) and new values introduced in order 0..2.

Original entry on oeis.org

24, 129, 1017, 8122, 65045, 518049, 4142271, 33102260, 264412286, 2112680676, 16879669489, 134861200228, 1077489437845, 8608751763524, 68780667761705, 549531541049837, 4390551455487162, 35078855924532667, 280266876696504422

Offset: 1

R. H. Hardin, Jul 26 2016

nonn

Row 6 of A275401.

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

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

Cf. A275401.

Empirical: a(n) = 2*a(n-1) +28*a(n-2) +137*a(n-3) +222*a(n-4) -178*a(n-5) -1692*a(n-6) -272*a(n-7) +217*a(n-8) +3612*a(n-9) -2256*a(n-10) +1680*a(n-11) -1648*a(n-12) +1472*a(n-13) -192*a(n-14) +512*a(n-15) -256*a(n-16) for n>17

cp's OEIS Frontend

A275395 Number of n X 2 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,0) or (-1,1) and new values introduced in order 0..2.

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A275396 Number of nX3 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,0) or (-1,1) and new values introduced in order 0..2.

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A275397 Number of nX4 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,0) or (-1,1) and new values introduced in order 0..2.

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A275398 Number of n X 5 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,0) or (-1,1) and new values introduced in order 0..2.

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A275399 Number of nX6 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,0) or (-1,1) and new values introduced in order 0..2.

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A275400 Number of nX7 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,0) or (-1,1) and new values introduced in order 0..2.

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A275402 Number of 3 X n 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,0) or (-1,1) and new values introduced in order 0..2.

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A275403 Number of 4_X_n 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,0) or (-1,1) and new values introduced in order 0..2.

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A275404 Number of 5 X n 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,0) or (-1,1) and new values introduced in order 0..2.

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A275405 Number of 6Xn 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,0) or (-1,1) and new values introduced in order 0..2.

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