A223062 -id:A223062 - cp's OEIS frontend

A223056 Number of n X 2 0..3 arrays with all horizontally or vertically connected equal values in a straight line, and new values 0..3 introduced in row major order.

2, 10, 114, 1473, 19360, 255045, 3361024, 44294253, 583749160, 7693175205, 101387647984, 1336178514333, 17609374162360, 232072328089365, 3058459941439744, 40307163247443213, 531204410117077960

Offset: 1

R. H. Hardin, Mar 13 2013

nonn

Column 2 of A223062.

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

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

Cf. A223062.

Empirical: a(n) = 18*a(n-1) - 71*a(n-2) + 102*a(n-3) - 48*a(n-4) for n>5.

Empirical g.f.: x*(2 - 26*x + 76*x^2 - 73*x^3 + 16*x^4) / ((1 - x)*(1 - 2*x)*(1 - 15*x + 24*x^2)). - Colin Barker, Aug 16 2018

A223057 Number of n X 3 0..3 arrays with all horizontally or vertically connected equal values in a straight line, and new values 0..3 introduced in row major order.

Original entry on oeis.org

5, 114, 4865, 213469, 9383963, 412602889, 18142309235, 797728639489, 35076656042963, 1542343995891289, 67817897342466755, 2981998328788355809, 131120462107713937763, 5765454466967090614489, 253510891259359153159475

Offset: 1

R. H. Hardin, Mar 13 2013

nonn

Column 3 of A223062.

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

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

Cf. A223062.

Empirical: a(n) = 55*a(n-1) - 515*a(n-2) + 1337*a(n-3) - 696*a(n-4) - 1188*a(n-5) + 1008*a(n-6) for n>7.

Empirical g.f.: x*(5 - 161*x + 1170*x^2 - 2081*x^3 - 295*x^4 + 2238*x^5 - 336*x^6) / ((1 - x)*(1 - 2*x)*(1 - 52*x + 357*x^2 - 162*x^3 - 504*x^4)). - Colin Barker, Aug 17 2018

A223058 Number of nX4 0..3 arrays with all horizontally or vertically connected equal values in a straight line, and new values 0..3 introduced in row major order.

Original entry on oeis.org

15, 1473, 213469, 31331820, 4606719559, 677531592132, 99653055754459, 14657362298142480, 2155865978887475959, 317093854966287823308, 46639503202294456685971, 6859935143940031077127272

Offset: 1

R. H. Hardin Mar 13 2013

nonn

Column 4 of A223062

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

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

Empirical: a(n) = 200*a(n-1) -8673*a(n-2) +135916*a(n-3) -736271*a(n-4) -465544*a(n-5) +16580061*a(n-6) -48454316*a(n-7) +18185748*a(n-8) +126046080*a(n-9) -200199168*a(n-10) +88915968*a(n-11) for n>12

A223059 Number of nX5 0..3 arrays with all horizontally or vertically connected equal values in a straight line, and new values 0..3 introduced in row major order.

Original entry on oeis.org

51, 19360, 9383963, 4606719559, 2266567594841, 1115636153544055, 549172612438350029, 270334270159303305523, 133074373792931796543737, 65507037468442048450168351, 32246421320132829050759287877

Offset: 1

R. H. Hardin Mar 13 2013

nonn

Column 5 of A223062

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

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

A223060 Number of n X 6 0..3 arrays with all horizontally or vertically connected equal values in a straight line, and new values 0..3 introduced in row major order.

Original entry on oeis.org

187, 255045, 412602889, 677531592132, 1115636153544055, 1837966217755803448, 3028264612325675509047, 4989509449716896144976736, 8220974979731088191278751151, 13545313950246233778034214834568

Offset: 1

R. H. Hardin, Mar 13 2013

nonn

Column 6 of A223062.

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

R. H. Hardin, Table of n, a(n) for n = 1..111

Cf. A223062.

A223061 Number of nX7 0..3 arrays with all horizontally or vertically connected equal values in a straight line, and new values 0..3 introduced in row major order.

Original entry on oeis.org

715, 3361024, 18142309235, 99653055754459, 549172612438350029, 3028264612325675509047, 16700483735732492103987445, 92103002955687502077421475679, 507949261500434438520234512887781

Offset: 1

R. H. Hardin Mar 13 2013

nonn

Column 7 of A223062

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

R. H. Hardin, Table of n, a(n) for n = 1..25

A223055 Number of n X n 0..3 arrays with all horizontally or vertically connected equal values in a straight line, and new values 0..3 introduced in row major order.

Original entry on oeis.org

1, 10, 4865, 31331820, 2266567594841, 1837966217755803448, 16700483735732492103987445, 1700203937054371815103811136350852

Offset: 1

R. H. Hardin Mar 13 2013

nonn

Diagonal of A223062

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

cp's OEIS Frontend

A223056 Number of n X 2 0..3 arrays with all horizontally or vertically connected equal values in a straight line, and new values 0..3 introduced in row major order.

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A223057 Number of n X 3 0..3 arrays with all horizontally or vertically connected equal values in a straight line, and new values 0..3 introduced in row major order.

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A223058 Number of nX4 0..3 arrays with all horizontally or vertically connected equal values in a straight line, and new values 0..3 introduced in row major order.

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A223059 Number of nX5 0..3 arrays with all horizontally or vertically connected equal values in a straight line, and new values 0..3 introduced in row major order.

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A223060 Number of n X 6 0..3 arrays with all horizontally or vertically connected equal values in a straight line, and new values 0..3 introduced in row major order.

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A223061 Number of nX7 0..3 arrays with all horizontally or vertically connected equal values in a straight line, and new values 0..3 introduced in row major order.

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A223055 Number of n X n 0..3 arrays with all horizontally or vertically connected equal values in a straight line, and new values 0..3 introduced in row major order.

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