A183603 -id:A183603 - cp's OEIS frontend

A183596 1/6 the number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock containing all three values.

27, 204, 1479, 10797, 78729, 574185, 4187499, 30539367, 222722937, 1624313781, 11846086563, 86393262903, 630064268913, 4595045605149, 33511572001131, 244399197416799, 1782398262186441, 12998993444433333, 94801388754240819

Offset: 1

R. H. Hardin, Jan 05 2011

nonn

Column 2 of A183603.

			Some solutions with a(1,1)=0 for 5 X 3:
..0..2..1....0..2..1....0..0..2....0..0..2....0..2..0....0..2..0....0..1..2
..0..1..0....1..0..1....2..1..1....2..1..0....1..2..1....0..1..0....0..2..0
..1..2..2....1..2..0....1..0..2....0..1..2....2..0..0....1..2..1....1..2..1
..0..1..0....0..2..1....2..0..1....2..0..1....1..2..1....2..0..2....1..0..1
..0..2..2....1..1..0....2..1..2....1..2..1....0..1..0....1..1..2....0..2..1

R. H. Hardin, Table of n, a(n) for n = 1..200

Cf. A183603.

Empirical: a(n) = 8*a(n-1) - 3*a(n-2) - 16*a(n-3) + 2*a(n-4).

Empirical g.f.: 3*x*(9 - 4*x - 24*x^2 + 3*x^3) / (1 - 8*x + 3*x^2 + 16*x^3 - 2*x^4). - Colin Barker, Mar 30 2018

A183597 1/6 the number of (n+1) X 4 0..2 arrays with every 2 X 2 subblock containing all three values.

Original entry on oeis.org

120, 1479, 17174, 201770, 2366412, 27768032, 325834456, 3823553752, 44868561272, 526526214848, 6178727749808, 72506794636336, 850861000923008, 9984783537547136, 117170625132737568, 1374987868096008576

Offset: 1

R. H. Hardin, Jan 05 2011

nonn

Column 3 of A183603.

			Some solutions with a(1,1)=0 for 3 X 4:
..0..2..2..1....0..0..0..0....0..1..2..0....0..0..0..1....0..1..2..1
..2..1..0..2....2..1..2..1....2..0..1..0....2..1..2..2....2..2..0..0
..0..0..2..1....2..0..2..0....0..1..2..1....0..1..0..1....1..0..1..2

R. H. Hardin, Table of n, a(n) for n = 1..200

Cf. A183603.

Empirical: a(n) = 12*a(n-1) + 20*a(n-2) - 238*a(n-3) - 420*a(n-4) + 324*a(n-5) + 400*a(n-6) - 224*a(n-7).

Empirical g.f.: x*(120 + 39*x - 2974*x^2 - 5338*x^3 + 4094*x^4 + 5400*x^5 - 3024*x^6) / (1 - 12*x - 20*x^2 + 238*x^3 + 420*x^4 - 324*x^5 - 400*x^6 + 224*x^7). - Colin Barker, Mar 30 2018

A183598 1/6 the number of (n+1)X5 0..2 arrays with every 2X2 subblock containing all three values.

Original entry on oeis.org

534, 10797, 201770, 3831324, 72592860, 1376627608, 26108240340, 495215814566, 9393691937690, 178194216929170, 3380332407037684, 64125402470512942, 1216476053110547726, 23076960013228726054, 437778595866783333858

Offset: 1

R. H. Hardin Jan 05 2011

nonn

Column 4 of A183603

			Some solutions with a(1,1)=0 for 3X5
..0..2..0..2..1....0..2..1..1..2....0..2..1..1..0....0..0..0..1..2
..0..1..1..0..0....1..1..0..2..0....1..0..2..0..2....2..1..2..1..0
..2..2..0..2..1....0..2..1..1..1....1..2..1..2..1....1..0..0..0..2

R. H. Hardin, Table of n, a(n) for n = 1..200

Empirical: a(n)=29*a(n-1)-116*a(n-2)-2075*a(n-3)+10702*a(n-4)+51511*a(n-5)-261497*a(n-6)-510094*a(n-7)+2707193*a(n-8)+1565260*a(n-9)-12569843*a(n-10)+2644843*a(n-11)+22771798*a(n-12)-13641330*a(n-13)-14269732*a(n-14)+12528656*a(n-15)+1720808*a(n-16)-3240288*a(n-17)+392640*a(n-18)+109056*a(n-19)

A183599 1/6 the number of (n+1)X6 0..2 arrays with every 2X2 subblock containing all three values.

Original entry on oeis.org

2376, 78729, 2366412, 72592860, 2220901926, 68026656422, 2083981368760, 63854542807704, 1956721189681174, 59964037003007332, 1837667093496854518, 56318507579345070520, 1725998009645259021660, 52897152711871651813326

Offset: 1

R. H. Hardin Jan 05 2011

nonn

Column 5 of A183603

			Some solutions with a(1,1)=0 for 3X6
..0..1..2..1..0..1....0..1..0..1..1..1....0..1..0..2..1..2....0..1..0..0..1..0
..2..2..0..0..2..2....2..2..0..2..0..2....1..2..1..0..1..0....2..0..2..1..2..2
..0..1..1..2..1..0....1..0..1..1..1..1....1..0..2..2..1..2....1..1..1..0..0..1

R. H. Hardin, Table of n, a(n) for n = 1..200

A183600 1/6 the number of (n+1)X7 0..2 arrays with every 2X2 subblock containing all three values.

Original entry on oeis.org

10572, 574185, 27768032, 1376627608, 68026656422, 3366668183708, 166653005250320, 8251614370134644, 408619818725184342, 20236484168674868650, 1002238533164802053394, 49638595435230968839084

Offset: 1

R. H. Hardin Jan 05 2011

nonn

Column 6 of A183603

			Some solutions with a(1,1)=0 for 3X7
..0..0..2..0..1..1..2....0..0..0..1..2..2..0....0..0..0..0..1..0..1
..1..2..1..0..2..0..1....1..2..1..2..0..1..0....1..2..1..2..2..0..2
..2..0..2..0..1..0..2....2..0..0..1..2..0..2....0..0..0..1..0..1..0

R. H. Hardin, Table of n, a(n) for n = 1..200

A183601 1/6 the number of (n+1)X8 0..2 arrays with every 2X2 subblock containing all three values.

Original entry on oeis.org

47040, 4187499, 325834456, 26108240340, 2083981368760, 166653005250320, 13330538464876654, 1066653925785997106, 85362766209466105480, 6832162755933155019668, 546857478389624808674648

Offset: 1

R. H. Hardin Jan 05 2011

nonn

Column 7 of A183603

			Some solutions with a(1,1)=0 for 3X8
..0..0..0..1..0..1..0..2....0..0..0..1..0..2..1..0....0..0..0..0..0..1..2..1
..2..1..2..1..2..1..2..1....2..1..2..2..1..0..1..2....2..1..2..1..2..0..2..0
..1..0..0..0..2..0..1..0....1..0..0..1..0..2..0..2....0..1..0..0..0..1..1..0

R. H. Hardin, Table of n, a(n) for n = 1..118

A183602 1/6 the number of (n+1)X9 0..2 arrays with every 2X2 subblock containing all three values.

Original entry on oeis.org

209304, 30539367, 3823553752, 495215814566, 63854542807704, 8251614370134644, 1066653925785997106, 137936054886331468840, 17840841964756696807680, 2307848389145766144487866, 298559730522953008074518020

Offset: 1

R. H. Hardin Jan 05 2011

nonn

Column 8 of A183603

			Some solutions with a(1,1)=0 for 3X9
..0..0..0..0..0..1..1..1..0....0..0..0..0..0..0..0..2..0
..1..2..1..2..1..2..0..2..1....1..2..1..2..1..2..1..1..2
..2..0..0..0..0..0..1..2..0....0..2..0..0..1..0..2..0..2

R. H. Hardin, Table of n, a(n) for n = 1..40

A183595 1/6 the number of (n+1)X(n+1) 0..2 arrays with every 2X2 subblock containing all three values.

Original entry on oeis.org

6, 204, 17174, 3831324, 2220901926, 3366668183708, 13330538464876654, 137936054886331468840, 3729575155642883493035294

Offset: 1

R. H. Hardin Jan 05 2011

nonn

Diagonal of A183603

			Some solutions with a(1,1)=0 for 3X3
..0..0..0....0..2..1....0..1..0....0..2..0....0..2..0....0..2..0....0..0..1
..1..2..1....2..1..0....2..0..2....1..0..1....1..1..1....2..1..2....1..2..1
..0..0..0....0..1..2....1..1..1....2..2..1....2..0..2....1..0..2....2..0..2

cp's OEIS Frontend

A183596 1/6 the number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock containing all three values.

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A183597 1/6 the number of (n+1) X 4 0..2 arrays with every 2 X 2 subblock containing all three values.

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A183598 1/6 the number of (n+1)X5 0..2 arrays with every 2X2 subblock containing all three values.

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A183599 1/6 the number of (n+1)X6 0..2 arrays with every 2X2 subblock containing all three values.

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A183600 1/6 the number of (n+1)X7 0..2 arrays with every 2X2 subblock containing all three values.

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A183601 1/6 the number of (n+1)X8 0..2 arrays with every 2X2 subblock containing all three values.

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A183602 1/6 the number of (n+1)X9 0..2 arrays with every 2X2 subblock containing all three values.

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A183595 1/6 the number of (n+1)X(n+1) 0..2 arrays with every 2X2 subblock containing all three values.

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