A268423 -id:A268423 - cp's OEIS frontend

A268419 Number of n X 1 0..3 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.

1, 2, 5, 14, 44, 147, 505, 1750, 6065, 20950, 72052, 246715, 841345, 2858714, 9682221, 32700942, 110173948, 370393059, 1242869721, 4163561358, 13927246329, 46526402422, 155249799428, 517505902283, 1723457914689, 5734951039346

Offset: 1

R. H. Hardin, Feb 04 2016

nonn

			Some solutions for n=8:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....1....1....1....0....1....1....1....1....0....1....1....1....1....0....1
..0....2....1....2....0....0....1....2....0....1....0....2....0....2....0....0
..1....2....0....2....0....1....1....1....2....2....2....0....2....1....1....1
..2....3....2....1....0....2....0....2....3....0....1....0....0....3....0....1
..0....0....3....0....0....1....1....3....3....2....3....2....3....0....2....1
..3....2....0....3....0....0....2....3....3....0....1....0....2....2....1....2
..0....2....3....2....1....3....3....2....1....1....0....2....2....0....0....1

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

Column 1 of A268423.

Empirical: a(n) = 8*a(n-1) - 20*a(n-2) + 12*a(n-3) + 12*a(n-4) - 8*a(n-5) - 3*a(n-6).

Empirical g.f.: x*(1 - 6*x + 9*x^2 + 2*x^3 - 4*x^4 - x^5) / ((1 - x)*(1 - 3*x)*(1 - x - x^2)*(1 - 3*x - x^2)). - Colin Barker, Jan 13 2019

A268420 Number of nX2 0..3 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.

Original entry on oeis.org

2, 15, 187, 2530, 34195, 448667, 5720450, 71224847, 869969995, 10461568690, 124193817155, 1458609678443, 16976365857602, 196066210076847, 2249518678962747, 25662410911209090, 291308117338854611

Offset: 1

R. H. Hardin, Feb 04 2016

nonn

Column 2 of A268423.

			Some solutions for n=5
..0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..0....0..1....0..1
..0..2....1..0....2..3....2..0....2..0....1..2....2..1....1..2....2..2....2..0
..2..1....2..2....2..0....3..3....2..2....1..1....3..1....0..2....3..2....0..0
..1..2....2..2....3..0....3..3....0..0....2..2....2..1....3..1....1..0....1..3
..3..2....0..0....2..3....2..1....3..2....0..0....0..3....0..0....0..2....3..1

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

Cf. A268423.

Empirical: a(n) = 33*a(n-1) -389*a(n-2) +1865*a(n-3) -2461*a(n-4) -3639*a(n-5) +7361*a(n-6) +2407*a(n-7) -5491*a(n-8) -585*a(n-9) +981*a(n-10) -81*a(n-11)

A268421 Number of nX4 0..3 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.

Original entry on oeis.org

12, 2191, 494098, 92967597, 15615613747, 2414369699870, 350815694801710, 48579100267639483, 6474432977080854160, 836528598526349043093, 105356335957177414141417, 12989039321265021304747296

Offset: 1

R. H. Hardin, Feb 04 2016

nonn

Column 4 of A268423.

			Some solutions for n=2
..0..1..0..2....0..0..1..2....0..1..2..2....0..1..0..2....0..0..1..2
..3..3..1..0....0..2..2..1....1..3..3..1....3..0..0..1....3..0..0..3

R. H. Hardin, Table of n, a(n) for n = 1..43

Cf. A268423.

A268424 Number of 4Xn 0..3 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.

Original entry on oeis.org

14, 2530, 467899, 92967597, 17282463434, 3197637400309, 577216284723410, 103129350712869051, 18199468798597838146, 3185845262388985273409, 553601961042772734126748, 95663189554686667773844253

Offset: 1

R. H. Hardin, Feb 04 2016

nonn

Row 4 of A268423.

			Some solutions for n=2
..0..1....0..1....0..1....0..1....0..1....0..0....0..0....0..1....0..0....0..1
..2..3....0..2....2..0....2..2....0..2....1..0....1..0....2..3....1..2....2..1
..2..2....0..0....2..0....2..2....2..2....2..3....0..2....0..1....3..0....0..0
..2..3....2..1....0..3....3..0....0..3....2..1....2..3....0..3....1..1....3..2

R. H. Hardin, Table of n, a(n) for n = 1..41

Cf. A268423.

A268422 Number of nX5 0..3 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.

Original entry on oeis.org

39, 30295, 25770278, 17282463434, 10053286458091, 5273786308929110, 2560363569664309507, 1170610262171483735817, 510268599126763954210436

Offset: 1

R. H. Hardin, Feb 04 2016

nonn

Column 5 of A268423.

			Some solutions for n=2
..0..0..1..2..3....0..0..1..0..2....0..1..1..0..0....0..1..2..2..1
..2..2..3..3..0....1..1..3..3..2....2..0..1..0..2....1..0..1..0..2

Cf. A268423.

A268425 Number of 5Xn 0..3 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.

Original entry on oeis.org

44, 34195, 22309009, 15615613747, 10053286458091, 6434348326690233, 3993182343091351469, 2446591845328690229717

Offset: 1

R. H. Hardin, Feb 04 2016

nonn

Row 5 of A268423.

			Some solutions for n=2
..0..1....0..1....0..1....0..0....0..0....0..0....0..1....0..1....0..1....0..1
..2..0....0..0....0..0....1..2....1..2....0..1....2..2....1..0....2..3....1..2
..1..2....0..2....1..2....1..0....1..0....1..2....2..0....1..0....0..3....2..3
..1..1....3..1....2..3....3..0....1..0....3..0....3..3....0..1....2..3....3..1
..3..0....2..0....0..3....0..0....1..2....2..1....2..3....2..0....1..3....2..0

Cf. A268423.

cp's OEIS Frontend

A268419 Number of n X 1 0..3 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.

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A268420 Number of nX2 0..3 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.

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A268421 Number of nX4 0..3 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.

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A268424 Number of 4Xn 0..3 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.

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A268422 Number of nX5 0..3 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.

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A268425 Number of 5Xn 0..3 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.

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