A204685 -id:A204685 - cp's OEIS frontend

A204678 Number of n X 1 0..3 arrays with no occurrence of three equal elements in a row horizontally, vertically, diagonally or antidiagonally, and new values 0..3 introduced in row major order.

1, 2, 4, 12, 40, 143, 528, 1979, 7466, 28246, 106992, 405481, 1537042, 5826959, 22091016, 83752328, 317527448, 1203835147, 4564081020, 17303737555, 65603438014, 248721498050, 942974761824, 3575088704597, 13554190277870

Offset: 1

R. H. Hardin, Jan 18 2012

nonn

Column 1 of A204685.

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

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

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

Empirical g.f.: x*(1 + x)*(1 - 3*x - 2*x^2 + 2*x^3 + x^4) / ((1 - x - x^2)*(1 - 3*x - 3*x^2)). - Colin Barker, Feb 19 2018

A204679 Number of n X 2 0..3 arrays with no occurrence of three equal elements in a row horizontally, vertically, diagonally or antidiagonally, and new values 0..3 introduced in row major order.

Original entry on oeis.org

2, 15, 159, 2191, 31168, 447343, 6427791, 92387812, 1327953799, 19087798375, 274365294336, 3943689122935, 56686048473223, 814797524429284, 11711788424726319, 168343648648695295, 2419748633865949120

Offset: 1

R. H. Hardin, Jan 18 2012

nonn

Column 2 of A204685.

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

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

Cf. A204685.

Empirical: a(n) = 14*a(n-1) +14*a(n-2) -124*a(n-3) -6*a(n-4) +90*a(n-5) -27*a(n-6) for n>8.

Empirical g.f.: x*(2 - 13*x - 79*x^2 + 3*x^3 + 140*x^4 - 57*x^5 - 21*x^6 + 9*x^7) / ((1 + x)*(1 + 3*x)*(1 - 3*x + x^2)*(1 - 15*x + 9*x^2)). - Colin Barker, Feb 23 2018

A204680 Number of nX3 0..3 arrays with no occurrence of three equal elements in a row horizontally, vertically, diagonally or antidiagonally, and new values 0..3 introduced in row major order.

Original entry on oeis.org

4, 159, 6451, 287379, 12711292, 563046972, 24932875448, 1104148318540, 48896363697435, 2165344586789384, 95890854634053213, 4246463765107286355, 188051863862618823831, 8327753561924846574597, 368789108809170527549222

Offset: 1

R. H. Hardin Jan 18 2012

nonn

Column 3 of A204685

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

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

Empirical: a(n) = 33*a(n-1) +576*a(n-2) -2576*a(n-3) -38824*a(n-4) +127580*a(n-5) +909748*a(n-6) -3116838*a(n-7) -7687952*a(n-8) +37104276*a(n-9) -63026296*a(n-10) -432695012*a(n-11) +2720629849*a(n-12) -5107909211*a(n-13) +3025539132*a(n-14) +16236494388*a(n-15) -61214998652*a(n-16) +60381991332*a(n-17) +26465066916*a(n-18) -101087636628*a(n-19) +92416374336*a(n-20) +14995740528*a(n-21) -85493406672*a(n-22) +58756380048*a(n-23) +4342368528*a(n-24) -38953846080*a(n-25) +13150955232*a(n-26) +1077909120*a(n-27) -6291032832*a(n-28) +3193509888*a(n-29) +1854296064*a(n-30) for n>33

A204681 Number of nX4 0..3 arrays with no occurrence of three equal elements in a row horizontally, vertically, diagonally or antidiagonally, and new values 0..3 introduced in row major order.

Original entry on oeis.org

12, 2191, 287379, 40919141, 5770321516, 815364171994, 115180678788869, 16271532972153414, 2298647402512667451, 324726122304981135405, 45873499136412060284740, 6480470930161792394441041

Offset: 1

R. H. Hardin Jan 18 2012

nonn

Column 4 of A204685

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

Ron Hardin, Table of n, a(n) for n = 1..73

A204677 Number of n X n 0..3 arrays with no occurrence of three equal elements in a row horizontally, vertically, diagonally or antidiagonally, and new values 0..3 introduced in row major order.

Original entry on oeis.org

1, 15, 6451, 40919141, 2579588216958

Offset: 1

R. H. Hardin, Jan 18 2012

nonn

Diagonal of A204685.

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

Cf. A204685.

A204682 Number of n X 5 0..3 arrays with no occurrence of three equal elements in a row horizontally, vertically, diagonally or antidiagonally, and new values 0..3 introduced in row major order.

Original entry on oeis.org

40, 31168, 12711292, 5770321516, 2579588216958, 1155411237719424, 517329649988490420, 231643442002878488571

Offset: 1

R. H. Hardin, Jan 18 2012

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

Column 5 of A204685.

A204683 Number of nX6 0..3 arrays with no occurrence of three equal elements in a row horizontally, vertically, diagonally or antidiagonally, and new values 0..3 introduced in row major order.

Original entry on oeis.org

143, 447343, 563046972, 815364171994, 1155411237719424

Offset: 1

R. H. Hardin Jan 18 2012

nonn

Column 6 of A204685

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

A204684 Number of nX7 0..3 arrays with no occurrence of three equal elements in a row horizontally, vertically, diagonally or antidiagonally, and new values 0..3 introduced in row major order.

Original entry on oeis.org

528, 6427791, 24932875448, 115180678788869, 517329649988490420

Offset: 1

R. H. Hardin Jan 18 2012

nonn

Column 7 of A204685

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

cp's OEIS Frontend

A204678 Number of n X 1 0..3 arrays with no occurrence of three equal elements in a row horizontally, vertically, diagonally or antidiagonally, and new values 0..3 introduced in row major order.

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A204679 Number of n X 2 0..3 arrays with no occurrence of three equal elements in a row horizontally, vertically, diagonally or antidiagonally, and new values 0..3 introduced in row major order.

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A204680 Number of nX3 0..3 arrays with no occurrence of three equal elements in a row horizontally, vertically, diagonally or antidiagonally, and new values 0..3 introduced in row major order.

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A204681 Number of nX4 0..3 arrays with no occurrence of three equal elements in a row horizontally, vertically, diagonally or antidiagonally, and new values 0..3 introduced in row major order.

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A204677 Number of n X n 0..3 arrays with no occurrence of three equal elements in a row horizontally, vertically, diagonally or antidiagonally, and new values 0..3 introduced in row major order.

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A204682 Number of n X 5 0..3 arrays with no occurrence of three equal elements in a row horizontally, vertically, diagonally or antidiagonally, and new values 0..3 introduced in row major order.

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A204683 Number of nX6 0..3 arrays with no occurrence of three equal elements in a row horizontally, vertically, diagonally or antidiagonally, and new values 0..3 introduced in row major order.

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A204684 Number of nX7 0..3 arrays with no occurrence of three equal elements in a row horizontally, vertically, diagonally or antidiagonally, and new values 0..3 introduced in row major order.

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