A275183 -id:A275183 - cp's OEIS frontend

A275178 Number of n X 3 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,0) or (-1,1) and new values introduced in order 0..2.

5, 16, 25, 41, 85, 181, 389, 834, 1781, 3799, 8110, 17328, 37032, 79130, 169059, 361178, 771648, 1648657, 3522441, 7525825, 16079113, 34353402, 73396957, 156814715, 335039190, 715820740, 1529371036, 3267543982, 6981199507

Offset: 1

R. H. Hardin, Jul 19 2016

nonn

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

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

Column 3 of A275183.

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

Empirical g.f.: x*(5 - 4*x - 9*x^2 + 12*x^3 - 4*x^4 - 17*x^5 + 11*x^6 + 5*x^7) / ((1 - x)*(1 - 3*x + 3*x^2 - 2*x^3 - x^4)). - Colin Barker, Feb 01 2019

A275179 Number of n X 4 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,0) or (-1,1) and new values introduced in order 0..2.

Original entry on oeis.org

14, 64, 89, 141, 353, 914, 2386, 6228, 16249, 42451, 111108, 291065, 762378, 1995896, 5223852, 13673069, 35794346, 93714905, 245360591, 642367172, 1681704625, 4402670689, 11526266952, 30176270194, 79002891883, 206832552922

Offset: 1

R. H. Hardin, Jul 19 2016

nonn

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

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

Column 4 of A275183.

Empirical: a(n) = 8*a(n-1) - 28*a(n-2) + 57*a(n-3) - 70*a(n-4) + 47*a(n-5) - 12*a(n-6) - a(n-7) - 2*a(n-8) + a(n-9) for n>12.

Empirical g.f.: x*(14 - 48*x - 31*x^2 + 423*x^3 - 951*x^4 + 787*x^5 + 311*x^6 - 920*x^7 + 378*x^8 + 125*x^9 + 29*x^10 - 32*x^11) / ((1 - 3*x + x^2)*(1 - 5*x + 12*x^2 - 16*x^3 + 10*x^4 - x^5 - x^6 - x^7)). - Colin Barker, Feb 01 2019

A275180 Number of n X 5 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,0) or (-1,1) and new values introduced in order 0..2.

Original entry on oeis.org

41, 256, 317, 482, 1465, 4603, 14643, 46799, 149772, 479722, 1538582, 4942028, 15891866, 51127466, 164489244, 529125544, 1701961499, 5474696445, 17611978722, 56660560468, 182287542046, 586443173365, 1886643497675, 6069534405199

Offset: 1

R. H. Hardin, Jul 19 2016

nonn

Column 5 of A275183.

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

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

Cf. A275183.

Empirical: a(n) = 16*a(n-1) -120*a(n-2) +561*a(n-3) -1820*a(n-4) +4313*a(n-5) -7688*a(n-6) +10549*a(n-7) -11473*a(n-8) +10333*a(n-9) -8076*a(n-10) +5538*a(n-11) -3198*a(n-12) +1466*a(n-13) -508*a(n-14) +120*a(n-15) -12*a(n-16) for n > 21.

A275181 Number of nX6 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,0) or (-1,1) and new values introduced in order 0..2.

Original entry on oeis.org

122, 1024, 1129, 1651, 6081, 23313, 90793, 355258, 1392050, 5466938, 21539426, 85093786, 336588196, 1331473727, 5265942503, 20828817622, 82420863039, 326283110365, 1291905762290, 5114955533848, 20248639590431, 80153872862995

Offset: 1

R. H. Hardin, Jul 19 2016

nonn

Column 6 of A275183.

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

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

Cf. A275183.

Empirical: a(n) = 32*a(n-1) -496*a(n-2) +4961*a(n-3) -35960*a(n-4) +201091*a(n-5) -902032*a(n-6) +3333981*a(n-7) -10358635*a(n-8) +27489359*a(n-9) -63147252*a(n-10) +127012656*a(n-11) -225853366*a(n-12) +357739737*a(n-13) -507298821*a(n-14) +645538311*a(n-15) -736806613*a(n-16) +752032038*a(n-17) -682548311*a(n-18) +546209109*a(n-19) -380703800*a(n-20) +226996531*a(n-21) -112609944*a(n-22) +44283885*a(n-23) -12407657*a(n-24) +1618639*a(n-25) +454684*a(n-26) -304782*a(n-27) +64173*a(n-28) +1145*a(n-29) -3123*a(n-30) +439*a(n-31) +34*a(n-32) -12*a(n-33) -a(n-34) for n>39

A275182 Number of nX7 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,0) or (-1,1) and new values introduced in order 0..2.

Original entry on oeis.org

365, 4096, 4021, 5653, 25241, 117916, 561044, 2688402, 12931103, 62408531, 302138208, 1466387881, 7128875693, 34691973269, 168923525976, 822823965071, 4008952988381, 19536216274450, 95219416747615, 464168982600409

Offset: 1

R. H. Hardin, Jul 19 2016

nonn

Column 7 of A275183.

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

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

Cf. A275183.

Empirical recurrence of order 67 (see link above)

A275184 Number of 4 X n 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,0) or (-1,1) and new values introduced in order 0..2.

Original entry on oeis.org

4, 12, 41, 141, 482, 1651, 5653, 19356, 66277, 226937, 777050, 2660679, 9110369, 31194604, 106812721, 365734965, 1252304626, 4287987275, 14682397949, 50273658876, 172140871373, 589423572097, 2018231606314, 6910580115135

Offset: 1

R. H. Hardin, Jul 19 2016

nonn

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

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

Row 4 of A275183.

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

Empirical g.f.: x*(4 + 4*x + x^2 - x^3) / (1 - 2*x - 4*x^2 - 3*x^3). - Colin Barker, Feb 01 2019

A275185 Number of 5 X n 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,0) or (-1,1) and new values introduced in order 0..2.

Original entry on oeis.org

8, 21, 85, 353, 1465, 6081, 25241, 104769, 434873, 1805057, 7492377, 31099137, 129085369, 535803713, 2223998105, 9231305153, 38317026745, 159045174401, 660159977241, 2740172389249, 11373826014393, 47210138571457

Offset: 1

R. H. Hardin, Jul 19 2016

nonn

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

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

Row 5 of A275183.

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

Empirical g.f.: x*(8 + 5*x - 13*x^2 - 28*x^3 - 4*x^4) / (1 - 2*x - 7*x^2 - 8*x^3). - Colin Barker, Feb 01 2019

A275186 Number of 6 X n 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,0) or (-1,1) and new values introduced in order 0..2.

Original entry on oeis.org

16, 37, 181, 914, 4603, 23313, 117916, 596625, 3018913, 15274618, 77286999, 391054261, 1978648444, 10011529573, 50656125413, 256308871218, 1296866472387, 6561859014441, 33201563019036, 167992603723721, 850005614599481

Offset: 1

R. H. Hardin, Jul 19 2016

nonn

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

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

Row 6 of A275183.

Empirical: a(n) = 2*a(n-1) + 12*a(n-2) + 19*a(n-3) - 4*a(n-4) - 12*a(n-5) - 16*a(n-6) for n>7.

Empirical g.f.: x*(16 + 5*x - 85*x^2 - 196*x^3 - 36*x^4 + 40*x^5 + 112*x^6) / ((1 - x)*(1 - x - 13*x^2 - 32*x^3 - 28*x^4 - 16*x^5)). - Colin Barker, Feb 01 2019

A275187 Number of 7 X n 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,0) or (-1,1) and new values introduced in order 0..2.

Original entry on oeis.org

32, 65, 389, 2386, 14643, 90793, 561044, 3472521, 21488129, 132962186, 822814111, 5091567885, 31507279460, 194970115869, 1206493799669, 7465907869266, 46199772632427, 285888830879985, 1769108624416628, 10947420840825089

Offset: 1

R. H. Hardin, Jul 19 2016

nonn

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

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

Row 7 of A275183.

Empirical: a(n) = 2*a(n-1) + 20*a(n-2) + 43*a(n-3) - 20*a(n-4) - 92*a(n-5) - 176*a(n-6) - 16*a(n-7) - 16*a(n-8) + 64*a(n-9) for n>10.

Empirical g.f.: x*(32 + x - 381*x^2 - 1068*x^3 - 64*x^4 + 1304*x^5 + 3392*x^6 + 384*x^7 + 496*x^8 - 1216*x^9) / (1 - 2*x - 20*x^2 - 43*x^3 + 20*x^4 + 92*x^5 + 176*x^6 + 16*x^7 + 16*x^8 - 64*x^9). - Colin Barker, Feb 01 2019

A275177 Number of n X n 0..2 arrays with no element equal to any value at offset (-2,-1), (-1,0) or (-1,1) and new values introduced in order 0..2.

Original entry on oeis.org

1, 4, 25, 141, 1465, 23313, 561044, 20397794, 1120217646, 93298660085, 11806084302586, 2272026396983803, 664988521276834246

Offset: 1

R. H. Hardin, Jul 19 2016

nonn

Diagonal of A275183.

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

Cf. A275183.

cp's OEIS Frontend

A275178 Number of n X 3 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,0) or (-1,1) and new values introduced in order 0..2.

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A275179 Number of n X 4 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,0) or (-1,1) and new values introduced in order 0..2.

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A275180 Number of n X 5 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,0) or (-1,1) and new values introduced in order 0..2.

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A275181 Number of nX6 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,0) or (-1,1) and new values introduced in order 0..2.

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A275182 Number of nX7 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,0) or (-1,1) and new values introduced in order 0..2.

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A275184 Number of 4 X n 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,0) or (-1,1) and new values introduced in order 0..2.

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A275185 Number of 5 X n 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,0) or (-1,1) and new values introduced in order 0..2.

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A275186 Number of 6 X n 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,0) or (-1,1) and new values introduced in order 0..2.

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A275187 Number of 7 X n 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,0) or (-1,1) and new values introduced in order 0..2.

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A275177 Number of n X n 0..2 arrays with no element equal to any value at offset (-2,-1), (-1,0) or (-1,1) and new values introduced in order 0..2.

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