A230739 -id:A230739 - cp's OEIS frontend

A230757 T(n,k)=Number of (n+3)X(k+3) 0..2 arrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero.

12, 192, 192, 2700, 5544, 2700, 31212, 178608, 178608, 31212, 363312, 4838400, 13305708, 4838400, 363312, 4120752, 129731328, 820317888, 820317888, 129731328, 4120752, 46949808, 3423037464, 51048476748, 116879941620, 51048476748

Offset: 1

R. H. Hardin, Oct 29 2013

Table starts
.......12.........192............2700..............31212................363312
......192........5544..........178608............4838400.............129731328
.....2700......178608........13305708..........820317888...........51048476748
....31212.....4838400.......820317888.......116879941620........17027460691212
...363312...129731328.....51048476748.....17027460691212......5769362600920812
..4120752..3423037464...3154520054700...2446111719135732...1928867953682733132
.46949808.90231813552.194576103540300.350956390609736652.645610139671314494208

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

R. H. Hardin, Table of n, a(n) for n = 1..180

Empirical for column k:
k=1: [order 15]
k=2: [order 36]
T(n,k)=3*A230708(n,k)*A230739(n,k)

A230735 Number of (n+3)X(n+3) 0..2 black square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero.

Original entry on oeis.org

2, 66, 2106, 320970, 43853402, 36695929036, 26681634560690, 121531720205091748, 479398570293769095556, 11869733818244916838154264

Offset: 1

R. H. Hardin, Oct 28 2013

nonn

Diagonal of A230739

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

A230736 Number of (n+3)X(2+3) 0..2 black square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero.

Original entry on oeis.org

8, 66, 244, 2016, 6576, 54138, 173428, 1427040, 4558536, 37506738, 119758148, 985334832, 3145930352, 25883741898, 82639468964, 679931791152, 2170826159272, 17860880147874, 57024624645332, 469180811419968, 1497958570841456

Offset: 1

R. H. Hardin, Oct 28 2013

nonn

Column 2 of A230739

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

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

Empirical: a(n) = 31*a(n-2) -126*a(n-4) +42*a(n-6) +79*a(n-8) -a(n-10) +8*a(n-12)

A230737 Number of (n+3)X(4+3) 0..2 black square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero.

Original entry on oeis.org

102, 2016, 16536, 320970, 2382398, 46599682, 342031378, 6692078688, 49068380730, 959928337654, 7037607186036, 137677370665624, 1009342929539188, 19745940646875492, 144761390761971996, 2831990839783724564

Offset: 1

R. H. Hardin, Oct 28 2013

nonn

Column 4 of A230739

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

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

Empirical: a(n) = 185*a(n-2) -6851*a(n-4) +145707*a(n-6) -2849231*a(n-8) +30720183*a(n-10) -36007996*a(n-12) -743385180*a(n-14) +287330815*a(n-16) +8627923017*a(n-18) -12118273932*a(n-20) -29408445279*a(n-22) +45675171837*a(n-24) -13807146112*a(n-26) -2411662568755*a(n-28) +3802259458200*a(n-30) +3456476952882*a(n-32) +4249525502473*a(n-34) -5769431443156*a(n-36) -7037014662528*a(n-38) +2632063276930*a(n-40) +18416679443602*a(n-42) +9430615399362*a(n-44) +259673859628*a(n-46) +64576080600*a(n-48) +325261872*a(n-50)

A230738 Number of (n+3)X(6+3) 0..2 black square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero.

Original entry on oeis.org

1172, 54138, 1025430, 46599682, 801845362, 36695929036, 625553036008, 28644012159382, 487784854592488, 22335960353679258, 380324726478587580, 17415157060199286942, 296532282288946047888, 13578285711710490028400

Offset: 1

R. H. Hardin, Oct 28 2013

nonn

Column 6 of A230739

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

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

cp's OEIS Frontend

A230757 T(n,k)=Number of (n+3)X(k+3) 0..2 arrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero.

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A230735 Number of (n+3)X(n+3) 0..2 black square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero.

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A230736 Number of (n+3)X(2+3) 0..2 black square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero.

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A230737 Number of (n+3)X(4+3) 0..2 black square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero.

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A230738 Number of (n+3)X(6+3) 0..2 black square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero.

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