A222924 -id:A222924 - cp's OEIS frontend

A222919 Number of n X 1 0..4 arrays with no three equal values in a row horizontally or vertically, and new values 0..4 introduced in row major order.

1, 2, 4, 12, 41, 158, 663, 2944, 13537, 63551, 301968, 1444795, 6940099, 33411718, 161058633, 776930015, 3749357128, 18098055047, 87370273487, 421820387606, 2036618058597, 9833358788859, 47478828272736, 229245800095323

Offset: 1

R. H. Hardin, Mar 09 2013

nonn

Column 1 of A222924.

			All solutions for n=3:
..0....0....0....0
..1....1....1....0
..2....1....0....1

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

Cf. A222924.

Empirical: a(n) = 7*a(n-1) - 7*a(n-2) - 20*a(n-3) + 10*a(n-4) + 24*a(n-5) + 8*a(n-6) for n>8.

Empirical g.f.: x*(1 + x)*(1 - 6*x + 3*x^2 + 15*x^3 - 9*x^5 - 3*x^6) / ((1 - x - x^2)*(1 - 2*x - 2*x^2)*(1 - 4*x - 4*x^2)). - Colin Barker, Mar 16 2018

A222920 Number of nX2 0..4 arrays with no three equal values in a row horizontally or vertically, and new values 0..4 introduced in row major order.

Original entry on oeis.org

2, 15, 174, 3183, 68076, 1543538, 35663142, 829049736, 19310392822, 450063924406, 10491666753024, 244592254688694, 5702297247404918, 132941283209423448, 3099351244544272614, 72257348464516101894, 1684586587434789765504

Offset: 1

R. H. Hardin Mar 09 2013

nonn

Column 2 of A222924

			Some solutions for n=3
..0..1....0..1....0..1....0..0....0..1....0..1....0..0....0..0....0..1....0..0
..0..0....1..0....0..2....1..0....2..2....2..0....1..2....1..2....2..3....1..1
..1..0....0..1....3..3....2..1....0..0....3..4....1..3....0..3....0..1....1..1

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

Empirical: a(n) = 28*a(n-1) -78*a(n-2) -789*a(n-3) +1250*a(n-4) +3796*a(n-5) -3288*a(n-6) -2208*a(n-7) +2432*a(n-8) -512*a(n-9) for n>11

A222921 Number of nX3 0..4 arrays with no three equal values in a row horizontally or vertically, and new values 0..4 introduced in row major order.

Original entry on oeis.org

4, 174, 13571, 1396408, 149478882, 16132176644, 1743046774975, 188375987615301, 20358991721595731, 2200340247114860719, 237806554693426088256, 25701465075957071507864, 2777742291970854979335967

Offset: 1

R. H. Hardin Mar 09 2013

nonn

Column 3 of A222924

			Some solutions for n=3
..0..0..1....0..1..2....0..1..0....0..1..2....0..1..1....0..1..1....0..0..1
..2..0..3....3..4..4....1..2..3....1..0..1....0..2..2....0..2..2....1..2..3
..0..3..1....3..3..1....1..0..3....1..3..4....1..3..3....3..3..1....4..1..2

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

Empirical: a(n) = 110*a(n-1) +152*a(n-2) -39692*a(n-3) +79710*a(n-4) +796150*a(n-5) -1333952*a(n-6) -1226634*a(n-7) -23628904*a(n-8) +55965332*a(n-9) +65773086*a(n-10) -123947190*a(n-11) -86026499*a(n-12) +40387328*a(n-13) +128788688*a(n-14) -15240812*a(n-15) -94039632*a(n-16) +31862080*a(n-17) +28558744*a(n-18) -10861760*a(n-19) -2218496*a(n-20) -2531712*a(n-21) -1928192*a(n-22) +635904*a(n-23) +317952*a(n-24)

A222922 Number of nX4 0..4 arrays with no three equal values in a row horizontally or vertically, and new values 0..4 introduced in row major order.

Original entry on oeis.org

12, 3183, 1396408, 700411548, 352790675074, 177991922235005, 89795579488204082, 45302597340251356553, 22855446389732416394860, 11530725901161434778153848, 5817327820706155068068660004

Offset: 1

R. H. Hardin Mar 09 2013

nonn

Column 4 of A222924

			Some solutions for n=3
..0..0..1..1....0..0..1..0....0..0..1..0....0..0..1..1....0..0..1..0
..2..3..0..3....1..2..2..1....2..2..3..0....2..0..0..1....1..2..0..1
..3..0..2..4....3..1..0..2....2..3..2..2....3..2..2..4....3..4..1..2

R. H. Hardin, Table of n, a(n) for n = 1..87

A222923 Number of nX5 0..4 arrays with no three equal values in a row horizontally or vertically, and new values 0..4 introduced in row major order.

Original entry on oeis.org

41, 68076, 149478882, 352790675074, 829048065675262, 1950399182366908036, 4587672845137864487256, 10791321299165218217699322, 25383677827763449530156884274, 59708321150765046377817427875602

Offset: 1

R. H. Hardin Mar 09 2013

nonn

Column 5 of A222924

			Some solutions for n=3
..0..0..1..1..0....0..0..1..0..2....0..0..1..2..0....0..0..1..0..2
..0..0..1..0..2....0..0..1..3..0....0..0..1..3..3....0..0..1..0..3
..2..3..4..2..4....1..3..0..1..1....1..3..4..3..3....1..3..4..1..0

R. H. Hardin, Table of n, a(n) for n = 1..12

cp's OEIS Frontend

A222919 Number of n X 1 0..4 arrays with no three equal values in a row horizontally or vertically, and new values 0..4 introduced in row major order.

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A222920 Number of nX2 0..4 arrays with no three equal values in a row horizontally or vertically, and new values 0..4 introduced in row major order.

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A222921 Number of nX3 0..4 arrays with no three equal values in a row horizontally or vertically, and new values 0..4 introduced in row major order.

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A222922 Number of nX4 0..4 arrays with no three equal values in a row horizontally or vertically, and new values 0..4 introduced in row major order.

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A222923 Number of nX5 0..4 arrays with no three equal values in a row horizontally or vertically, and new values 0..4 introduced in row major order.

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