A199133 -id:A199133 - cp's OEIS frontend

A199126 Number of nX1 0..2 arrays with values 0..2 introduced in row major order, the number of instances of each value within one of each other, and no element equal to any horizontal or vertical neighbor.

1, 1, 1, 3, 6, 5, 19, 37, 29, 124, 240, 182, 834, 1614, 1198, 5746, 11137, 8142, 40336, 78332, 56620, 287358, 559134, 400598, 2071558, 4038130, 2872754, 15079270, 29443040, 20824778, 110653854, 216379650, 152303410, 817542980, 1600817660

Offset: 1

R. H. Hardin Nov 03 2011

nonn

Column 1 of A199133

			All solutions for n=5
..0....0....0....0....0....0
..1....1....1....1....1....1
..2....2....2....0....2....0
..0....1....0....2....1....1
..2....2....1....1....0....2

R. H. Hardin, Table of n, a(n) for n = 1..200

Conjecture: a(3n) = A190917(n). - R. J. Mathar, Nov 01 2015

A199127 Number of n X 2 0..2 arrays with values 0..2 introduced in row major order, the number of instances of each value within one of each other, and no element equal to any horizontal or vertical neighbor.

Original entry on oeis.org

1, 2, 2, 12, 30, 30, 210, 560, 560, 4200, 11550, 11550, 90090, 252252, 252252, 2018016, 5717712, 5717712, 46558512, 133024320, 133024320, 1097450640, 3155170590, 3155170590, 26293088250, 75957810500, 75957810500, 638045608200

Offset: 1

R. H. Hardin, Nov 03 2011

nonn

Column 2 of A199133.

a(n) is the last term in row n of triangle in A286030 (see also formulas below). Bob Selcoe, Sep 26 2021

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

R. H. Hardin, Table of n, a(n) for n = 1..198

Cf. A286030.

Conjecture: a(3n+2) = a(3n+3) = A208881(n+1). - R. J. Mathar, Nov 01 2015
Conjecture: -(458*n-1205) *(n+2) *(n+1)*a(n) +(-208*n^3+2578*n^2-4613*n-2410) *a(n-1) +9*(-339*n-638) *a(n-2) +27*(n-2) *(458*n^2-289*n-1146) *a(n-3) +54*(n-2) *(n-3) *(104*n-1081) *a(n-4)=0. - R. J. Mathar, Nov 01 2015
Conjecture: (n+2)*(n+1)*a(n) +(5*n^2-2)*a(n-1) +3*(5*n^2-15*n+3) *a(n-2) +3*(n^2 -60*n +81)*a(n-3) +135*(-n^2+3*n-1)*a(n-4) -405*(n-2)*(n-4) *a(n-5) -810*(n-4) *(n-5) *a(n-6)=0. - R. J. Mathar, Nov 01 2015
From Bob Selcoe, Sep 26 2021: (Start)
When n == 0 (mod 3), a(n) = n!/(3*(n/3)!^3);
when n == 1 (mod 3), a(n) = n!/(((n+2)/3)!*((n-1)/3)!^2);
when n == 2 (mod 3), a(n) = n!/(((n-2)/3)!*((n+1)/3)!^2).
(End)

A199128 Number of nX3 0..2 arrays with values 0..2 introduced in row major order, the number of instances of each value within one of each other, and no element equal to any horizontal or vertical neighbor.

Original entry on oeis.org

1, 2, 6, 19, 70, 264, 1038, 4155, 16896, 69584, 289146, 1211873, 5111178, 21686612, 92453594, 395888507, 1701506820, 7337867736, 31739124866, 137656095241, 598476364166, 2607710997676, 11385288787534, 49800060551081

Offset: 1

R. H. Hardin Nov 03 2011

nonn

Column 3 of A199133

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

R. H. Hardin, Table of n, a(n) for n = 1..130

A199129 Number of nX4 0..2 arrays with values 0..2 introduced in row major order, the number of instances of each value within one of each other, and no element equal to any horizontal or vertical neighbor.

Original entry on oeis.org

3, 12, 19, 258, 1409, 2836, 48320, 295092, 629776, 11499816, 73045294, 159683856, 3012721252, 19537447260, 43276955012, 832789320948, 5471578311520, 12222775051564, 238366172778672, 1580313985819656, 3551105861275344

Offset: 1

R. H. Hardin Nov 03 2011

nonn

Column 4 of A199133

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

R. H. Hardin, Table of n, a(n) for n = 1..75

A199130 Number of nX5 0..2 arrays with values 0..2 introduced in row major order, the number of instances of each value within one of each other, and no element equal to any horizontal or vertical neighbor.

Original entry on oeis.org

6, 30, 70, 1409, 11475, 33970, 887966, 8181546, 26354800, 739462036, 7166709232, 23742940530, 690068431668, 6837489856538, 23031293598718, 682253330136338, 6857414650447522, 23326710623207736, 700022706564351432

Offset: 1

R. H. Hardin Nov 03 2011

nonn

Column 5 of A199133

			Some solutions for n=6
..0..1..2..1..2....0..1..2..1..0....0..1..0..2..0....0..1..0..1..0
..1..2..1..0..1....2..0..1..0..2....1..2..1..0..2....1..0..1..0..1
..0..1..0..2..0....0..1..2..1..0....0..1..0..2..0....2..1..2..1..2
..2..0..2..1..2....1..2..1..0..1....1..2..1..0..1....1..2..0..2..0
..0..2..0..2..1....2..0..2..1..2....2..0..2..1..2....2..1..2..0..2
..1..0..2..1..0....0..2..1..2..0....1..2..0..2..1....0..2..1..2..0

R. H. Hardin, Table of n, a(n) for n = 1..48

A199131 Number of nX6 0..2 arrays with values 0..2 introduced in row major order, the number of instances of each value within one of each other, and no element equal to any horizontal or vertical neighbor.

Original entry on oeis.org

5, 30, 264, 2836, 33970, 438502, 5926852, 82908094, 1187201812, 17307138986, 255687902462, 3817658150424, 57485010058768, 871667490461400, 13295046323445896, 203799010704532580, 3137556683409570358

Offset: 1

R. H. Hardin Nov 03 2011

nonn

Column 6 of A199133

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

R. H. Hardin, Table of n, a(n) for n = 1..34

A199132 Number of nX7 0..2 arrays with values 0..2 introduced in row major order, the number of instances of each value within one of each other, and no element equal to any horizontal or vertical neighbor.

Original entry on oeis.org

19, 210, 1038, 48320, 887966, 5926852, 358599045, 7633754680, 56435001338, 3718131446504, 84113596169937, 647071266317908, 44371190146396476, 1031280656608709860, 8107333731404729122, 567373010032314560752

Offset: 1

R. H. Hardin Nov 03 2011

nonn

Column 7 of A199133

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

R. H. Hardin, Table of n, a(n) for n = 1..22

A199125 Number of n X n 0..2 arrays with values 0..2 introduced in row major order, the number of instances of each value within one of each other, and no element equal to any horizontal or vertical neighbor.

Original entry on oeis.org

1, 2, 6, 258, 11475, 438502, 358599045, 247746055048, 141388449764548

Offset: 1

R. H. Hardin Nov 03 2011

nonn

Diagonal of A199133

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

cp's OEIS Frontend

A199126 Number of nX1 0..2 arrays with values 0..2 introduced in row major order, the number of instances of each value within one of each other, and no element equal to any horizontal or vertical neighbor.

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A199127 Number of n X 2 0..2 arrays with values 0..2 introduced in row major order, the number of instances of each value within one of each other, and no element equal to any horizontal or vertical neighbor.

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A199128 Number of nX3 0..2 arrays with values 0..2 introduced in row major order, the number of instances of each value within one of each other, and no element equal to any horizontal or vertical neighbor.

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A199129 Number of nX4 0..2 arrays with values 0..2 introduced in row major order, the number of instances of each value within one of each other, and no element equal to any horizontal or vertical neighbor.

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A199130 Number of nX5 0..2 arrays with values 0..2 introduced in row major order, the number of instances of each value within one of each other, and no element equal to any horizontal or vertical neighbor.

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A199131 Number of nX6 0..2 arrays with values 0..2 introduced in row major order, the number of instances of each value within one of each other, and no element equal to any horizontal or vertical neighbor.

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A199132 Number of nX7 0..2 arrays with values 0..2 introduced in row major order, the number of instances of each value within one of each other, and no element equal to any horizontal or vertical neighbor.

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A199125 Number of n X n 0..2 arrays with values 0..2 introduced in row major order, the number of instances of each value within one of each other, and no element equal to any horizontal or vertical neighbor.

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