A233073 -id:A233073 - cp's OEIS frontend

A233067 Number of n X n 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 in row major order.

1, 9, 582, 164495, 194998895, 975239425635, 20656955820980290, 1857471420698911806909, 710147877110621514637926027, 1155599363385647621950232861908393

Offset: 1

R. H. Hardin, Dec 03 2013

nonn

Diagonal of A233073

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

R. H. Hardin, Table of n, a(n) for n = 1..11

A233068 Number of n X 3 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 in row major order.

Original entry on oeis.org

5, 50, 582, 6854, 80811, 952869, 11235652, 132484030, 1562171807, 18420188169, 217199754056, 2561088558394, 30198812298187, 356086188910685, 4198753668883532, 49509171995392534, 583782308982449751

Offset: 1

R. H. Hardin, Dec 03 2013

nonn

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

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

Column 3 of A233073.

Empirical: a(n) = 14*a(n-1) - 28*a(n-2) + 24*a(n-3) - 11*a(n-4) + 2*a(n-5) for n>6.

Empirical g.f.: x*(5 - 20*x + 22*x^2 - 14*x^3 + 6*x^4 - x^5) / ((1 - x)*(1 - 13*x + 15*x^2 - 9*x^3 + 2*x^4)). - Colin Barker, Oct 07 2018

A233069 Number of nX4 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 in row major order.

Original entry on oeis.org

14, 289, 6854, 164495, 3957778, 95264272, 2293174089, 55201144642, 1328800293991, 31986846738550, 769986578444547, 18535097820450198, 446176415304028392, 10740347610658418594, 258541381485766745236

Offset: 1

R. H. Hardin, Dec 03 2013

nonn

Column 4 of A233073

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

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

Empirical: a(n) = 30*a(n-1) -155*a(n-2) +312*a(n-3) -393*a(n-4) +247*a(n-5) +43*a(n-6) -112*a(n-7) +15*a(n-8) +22*a(n-9) -9*a(n-10) +a(n-11) for n>12

A233070 Number of nX5 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 in row major order.

Original entry on oeis.org

41, 1682, 80811, 3957778, 194998895, 9622519979, 475027244071, 23452561697310, 1157902539075279, 57168401542703366, 2822543431496611477, 139355894459526629065, 6880342889895213536639, 339699437967530482926608

Offset: 1

R. H. Hardin, Dec 03 2013

nonn

Column 5 of A233073

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

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

Empirical: a(n) = 67*a(n-1) -957*a(n-2) +4487*a(n-3) -10440*a(n-4) +9842*a(n-5) +34671*a(n-6) -145789*a(n-7) +111684*a(n-8) +296032*a(n-9) -481473*a(n-10) -167907*a(n-11) +608240*a(n-12) -12730*a(n-13) -416027*a(n-14) +59065*a(n-15) +178117*a(n-16) -40627*a(n-17) -41054*a(n-18) +13432*a(n-19) +2184*a(n-20) -816*a(n-21) for n>23

A233071 Number of nX6 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 in row major order.

Original entry on oeis.org

122, 9801, 952869, 95264272, 9622519979, 975239425635, 98950914937033, 10043490383783484, 1019526537402445651, 103496939942560822667, 10506573357624046461778, 1066586510863326927801797

Offset: 1

R. H. Hardin, Dec 03 2013

nonn

Column 6 of A233073

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 58

Empirical recurrence of order 58 (see link above)

A233072 Number of nX7 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 in row major order.

Original entry on oeis.org

365, 57122, 11235652, 2293174089, 475027244071, 98950914937033, 20656955820980290, 4315955749032401626, 902039316691285768305, 188549438666892024287013, 39413397925167802927174270

Offset: 1

R. H. Hardin, Dec 03 2013

nonn

Column 7 of A233073

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

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

cp's OEIS Frontend

A233067 Number of n X n 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 in row major order.

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A233068 Number of n X 3 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 in row major order.

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A233069 Number of nX4 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 in row major order.

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A233070 Number of nX5 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 in row major order.

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A233071 Number of nX6 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 in row major order.

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A233072 Number of nX7 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 in row major order.

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