A204630 -id:A204630 - cp's OEIS frontend

A204623 Number of (n+1)X2 0..2 arrays with every 2X2 subblock having unequal diagonal elements or unequal antidiagonal elements, and new values 0..2 introduced in row major order.

12, 96, 768, 6144, 49152, 393216, 3145728, 25165824, 201326592, 1610612736, 12884901888, 103079215104, 824633720832, 6597069766656, 52776558133248, 422212465065984, 3377699720527872, 27021597764222976, 216172782113783808

Offset: 1

R. H. Hardin Jan 17 2012

nonn

Column 1 of A204630

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

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

Cf. A094085, A270568.

Empirical: a(n) = 8*a(n-1)

A204622 Number of (n+1)X(n+1) 0..2 arrays with every 2X2 subblock having unequal diagonal elements or unequal antidiagonal elements, and new values 0..2 introduced in row major order.

Original entry on oeis.org

12, 2049, 2490558, 21550390395, 1327448018292252, 582081449451902347866, 1816995451072561641887723586, 40376415985445663379679403072064855, 6387126785648912581213165822171077074078454

Offset: 1

R. H. Hardin Jan 17 2012

nonn

Diagonal of A204630

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

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

A204624 Number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock having unequal diagonal elements or unequal antidiagonal elements, and new values 0..2 introduced in row major order.

Original entry on oeis.org

96, 2049, 43734, 933462, 19923888, 425257068, 9076721064, 193734264456, 4135079723136, 88259474206608, 1883817316421472, 40208348322379872, 858210220662456576, 18317707978060726464, 390974632428061590144

Offset: 1

R. H. Hardin, Jan 17 2012

nonn

Column 2 of A204630.

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

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

Cf. A204630.

Empirical: a(n) = 22*a(n-1) -14*a(n-2).
Conjectures from Colin Barker, Jun 07 2018: (Start)
G.f.: 3*x*(32 - 21*x) / (1 - 22*x + 14*x^2).
a(n) = (3*(11+sqrt(107))^n*(31+3*sqrt(107)) + (11-sqrt(107))^n*(-93+9*sqrt(107))) / (4*sqrt(107)).
(End)

A204625 Number of (n+1) X 4 0..2 arrays with every 2 X 2 subblock having unequal diagonal elements or unequal antidiagonal elements, and new values 0..2 introduced in row major order.

Original entry on oeis.org

768, 43734, 2490558, 141832254, 8077061502, 459972403614, 26194503047262, 1491724252385406, 84950695233299262, 4837771196037723486, 275501337345598245918, 15689246928705157494846, 893471050128160321852158

Offset: 1

R. H. Hardin, Jan 17 2012

nonn

Column 3 of A204630.

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

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

Cf. A204630.

Empirical: a(n) = 60*a(n-1) - 175*a(n-2) + 68*a(n-3).

Empirical g.f.: 6*x*(128 - 391*x + 153*x^2) / (1 - 60*x + 175*x^2 - 68*x^3). - Colin Barker, Jun 07 2018

A204626 Number of (n+1)X5 0..2 arrays with every 2X2 subblock having unequal diagonal elements or unequal antidiagonal elements, and new values 0..2 introduced in row major order.

Original entry on oeis.org

6144, 933462, 141832254, 21550390395, 3274427479938, 497525810748759, 75595484720747496, 11486192649538372653, 1745244733464500021670, 265177441526573391694167, 40291813604266663731304284

Offset: 1

R. H. Hardin Jan 17 2012

nonn

Column 4 of A204630

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

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

Empirical: a(n) = 165*a(n-1) -2025*a(n-2) +6241*a(n-3) -270*a(n-4) -17282*a(n-5) +5524*a(n-6) +11864*a(n-7) +1568*a(n-8)

A204627 Number of (n+1)X6 0..2 arrays with every 2X2 subblock having unequal diagonal elements or unequal antidiagonal elements, and new values 0..2 introduced in row major order.

Original entry on oeis.org

49152, 19923888, 8077061502, 3274427479938, 1327448018292252, 538145459458960020, 218163372078770313246, 88443107870080810695504, 35854704917808122995732308, 14535444261320212706089532832

Offset: 1

R. H. Hardin Jan 17 2012

nonn

Column 5 of A204630

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

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

Empirical: a(n) = 460*a(n-1) -23188*a(n-2) +435694*a(n-3) -3658549*a(n-4) +11358936*a(n-5) +20419834*a(n-6) -191355445*a(n-7) +159553869*a(n-8) +865499344*a(n-9) -1132300188*a(n-10) -1371731191*a(n-11) +1522080017*a(n-12) +5670605*a(n-13) -262860202*a(n-14) +47382216*a(n-15)

A204628 Number of (n+1)X7 0..2 arrays with every 2X2 subblock having unequal diagonal elements or unequal antidiagonal elements, and new values 0..2 introduced in row major order.

Original entry on oeis.org

393216, 425257068, 459972403614, 497525810748759, 538145459458960020, 582081449451902347866, 629604521519860258105194, 681007535879068229405338152, 736607263887839663637635211744

Offset: 1

R. H. Hardin Jan 17 2012

nonn

Column 6 of A204630

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

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

A204629 Number of (n+1)X8 0..2 arrays with every 2X2 subblock having unequal diagonal elements or unequal antidiagonal elements, and new values 0..2 introduced in row major order.

Original entry on oeis.org

3145728, 9076721064, 26194503047262, 75595484720747496, 218163372078770313246, 629604521519860258105194, 1816995451072561641887723586, 5243724206237325303462055283538

Offset: 1

R. H. Hardin Jan 17 2012

nonn

Column 7 of A204630

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

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

cp's OEIS Frontend

A204623 Number of (n+1)X2 0..2 arrays with every 2X2 subblock having unequal diagonal elements or unequal antidiagonal elements, and new values 0..2 introduced in row major order.

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A204622 Number of (n+1)X(n+1) 0..2 arrays with every 2X2 subblock having unequal diagonal elements or unequal antidiagonal elements, and new values 0..2 introduced in row major order.

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A204624 Number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock having unequal diagonal elements or unequal antidiagonal elements, and new values 0..2 introduced in row major order.

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A204625 Number of (n+1) X 4 0..2 arrays with every 2 X 2 subblock having unequal diagonal elements or unequal antidiagonal elements, and new values 0..2 introduced in row major order.

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A204626 Number of (n+1)X5 0..2 arrays with every 2X2 subblock having unequal diagonal elements or unequal antidiagonal elements, and new values 0..2 introduced in row major order.

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A204627 Number of (n+1)X6 0..2 arrays with every 2X2 subblock having unequal diagonal elements or unequal antidiagonal elements, and new values 0..2 introduced in row major order.

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A204628 Number of (n+1)X7 0..2 arrays with every 2X2 subblock having unequal diagonal elements or unequal antidiagonal elements, and new values 0..2 introduced in row major order.

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A204629 Number of (n+1)X8 0..2 arrays with every 2X2 subblock having unequal diagonal elements or unequal antidiagonal elements, and new values 0..2 introduced in row major order.

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