A274803 -id:A274803 - cp's OEIS frontend

A274797 Number of n X n 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) (0,-1) or (-1,0) and new values introduced in order 0..2.

1, 3, 30, 596, 22988, 1774372, 273764292, 85071335388, 53278240463204, 67444355089828632, 172664716787589924632, 895256317336401964070392, 9404595196718819502562934668, 200324135427294084369446897344852

Offset: 1

R. H. Hardin, Jul 07 2016

nonn

Diagonal of A274803.

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

R. H. Hardin, Table of n, a(n) for n = 1..15

Cf. A274803.

A274798 Number of n X 3 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) (0,-1) or (-1,0) and new values introduced in order 0..2.

Original entry on oeis.org

2, 8, 30, 112, 420, 1572, 5888, 22048, 82568, 309200, 1157904, 4336144, 16238112, 60808896, 227718752, 852767104, 3193464512, 11958969152, 44784259584, 167709263104, 628042022016, 2351908141824, 8807486941952, 32982506778880

Offset: 1

R. H. Hardin, Jul 07 2016

nonn

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

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

Column 3 of A274803.

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

Empirical g.f.: 2*x*(1 + x)^2 / (1 - 2*x - 6*x^2 - 2*x^3). - Colin Barker, Jan 30 2019

A274799 Number of n X 4 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) (0,-1) or (-1,0) and new values introduced in order 0..2.

Original entry on oeis.org

4, 22, 112, 596, 3104, 16328, 85504, 448656, 2352080, 12335680, 64684112, 339207984, 1778768656, 9327806784, 48914391648, 256504556080, 1345094908224, 7053603314896, 36988695973168, 193966647764784, 1017150172662336

Offset: 1

R. H. Hardin, Jul 07 2016

nonn

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

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

Column 4 of A274803.

Empirical: a(n) = 2*a(n-1) + 15*a(n-2) + 11*a(n-3) - 2*a(n-4) - 2*a(n-5).

Empirical g.f.: 2*x*(2 + 7*x + 4*x^2 - x^3 - x^4) / (1 - 2*x - 15*x^2 - 11*x^3 + 2*x^4 + 2*x^5). - Colin Barker, Jan 31 2019

A274800 Number of n X 5 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) (0,-1) or (-1,0) and new values introduced in order 0..2.

Original entry on oeis.org

8, 60, 420, 3104, 22988, 169328, 1252608, 9243332, 68301192, 504334580, 3725379284, 27513045320, 203212320508, 1500856265992, 11085101613680, 81871796085532, 604688931568808, 4466096896968716, 32985652382855332

Offset: 1

R. H. Hardin, Jul 07 2016

nonn

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

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

Column 5 of A274803.

Empirical: a(n) = 2*a(n-1) + 35*a(n-2) + 42*a(n-3) - 41*a(n-4) - 60*a(n-5) - 23*a(n-6) - 2*a(n-7).

Empirical g.f.: 4*x*(2 + 11*x + 5*x^2 - 43*x^3 - 28*x^4 + 3*x^5 + 2*x^6) / (1 - 2*x - 35*x^2 - 42*x^3 + 41*x^4 + 60*x^5 + 23*x^6 + 2*x^7). - Colin Barker, Jan 31 2019

A274801 Number of n X 6 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) (0,-1) or (-1,0) and new values introduced in order 0..2.

Original entry on oeis.org

16, 164, 1572, 16328, 169328, 1774372, 18476064, 193292660, 2016460140, 21072173792, 219985654388, 2297904486000, 23995177354892, 250610794543168, 2617142836973944, 27332712382107996, 285444819027741180

Offset: 1

R. H. Hardin, Jul 07 2016

nonn

Column 6 of A274803.

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

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

Cf. A274803.

Empirical: a(n) = 2*a(n-1) +80*a(n-2) +140*a(n-3) -474*a(n-4) -998*a(n-5) -130*a(n-6) +781*a(n-7) +814*a(n-8) -79*a(n-9) -360*a(n-10) +54*a(n-11) +48*a(n-12) -52*a(n-13) +4*a(n-14) for n>15.

A274802 Number of nX7 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) (0,-1) or (-1,0) and new values introduced in order 0..2.

Original entry on oeis.org

32, 448, 5888, 85504, 1252608, 18476064, 273764292, 4044928780, 59936952948, 886462457880, 13127736774888, 194250101777432, 2875817749885724, 42561628448681904, 630035159343912668, 9325142535870239784

Offset: 1

R. H. Hardin, Jul 07 2016

nonn

Column 7 of A274803.

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

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

Cf. A274803.

Empirical: a(n) = 2*a(n-1) +182*a(n-2) +434*a(n-3) -4080*a(n-4) -11758*a(n-5) +15420*a(n-6) +64260*a(n-7) +38245*a(n-8) -87869*a(n-9) -225572*a(n-10) -13082*a(n-11) +255188*a(n-12) -3166*a(n-13) -19321*a(n-14) +49122*a(n-15) -82502*a(n-16) -88689*a(n-17) +115251*a(n-18) -9925*a(n-19) -4172*a(n-20) -937*a(n-21) -317*a(n-22) +140*a(n-23) -94*a(n-24) +6*a(n-25) for n>26

cp's OEIS Frontend

A274797 Number of n X n 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) (0,-1) or (-1,0) and new values introduced in order 0..2.

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A274798 Number of n X 3 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) (0,-1) or (-1,0) and new values introduced in order 0..2.

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A274799 Number of n X 4 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) (0,-1) or (-1,0) and new values introduced in order 0..2.

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A274800 Number of n X 5 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) (0,-1) or (-1,0) and new values introduced in order 0..2.

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A274801 Number of n X 6 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) (0,-1) or (-1,0) and new values introduced in order 0..2.

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A274802 Number of nX7 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) (0,-1) or (-1,0) and new values introduced in order 0..2.

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