A229606 -id:A229606 - cp's OEIS frontend

A229600 Number of defective 3-colorings of an n X 2 0..2 array connected horizontally and vertically with exactly two mistakes, and colors introduced in row-major 0..2 order.

0, 6, 39, 202, 925, 3924, 15795, 61182, 230121, 845640, 3049407, 10825650, 37929141, 131403708, 450839115, 1533738726, 5178892545, 17371743408, 57926537559, 192131864730, 634207340493, 2084322230820, 6822862231779, 22252658047182

Offset: 1

R. H. Hardin, Sep 26 2013

nonn

Column 2 of A229606.

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

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

Cf. A229606.

Empirical: a(n) = 9*a(n-1) - 27*a(n-2) + 27*a(n-3) for n>5.
Conjectures from Colin Barker, Mar 16 2018: (Start)
G.f.: x^2*(6 - 15*x + 13*x^2 - 2*x^3) / (1 - 3*x)^3.
a(n) = 3^(n-5) * (31*n+32*n^2-30) for n>2.
(End)

A229601 Number of defective 3-colorings of an n X 3 0..2 array connected horizontally and vertically with exactly two mistakes, and colors introduced in row-major 0..2 order.

Original entry on oeis.org

1, 39, 396, 3040, 20714, 131345, 792929, 4618048, 26165860, 145058507, 790042315, 4239980962, 22473980838, 117862612005, 612450538677, 3156938117780, 16157454978232, 82173962646319, 415564115855215, 2090880090793526

Offset: 1

R. H. Hardin, Sep 26 2013

nonn

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

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

Column 3 of A229606.

Empirical: a(n) = 15*a(n-1) - 81*a(n-2) + 185*a(n-3) - 162*a(n-4) + 60*a(n-5) - 8*a(n-6) for n>7.

Empirical g.f.: x*(1 + 24*x - 108*x^2 + 74*x^3 + 137*x^4 - 127*x^5 + 8*x^6) / (1 - 5*x + 2*x^2)^3. - Colin Barker, Sep 19 2018

A229602 Number of defective 3-colorings of an n X 4 0..2 array connected horizontally and vertically with exactly two mistakes, and colors introduced in row-major 0..2 order.

Original entry on oeis.org

3, 202, 3040, 35182, 362100, 3476928, 31848813, 281845934, 2429033768, 20498682291, 170050970491, 1390738347774, 11237781105036, 89873465482971, 712350529942518, 5602092417764388, 43752038622648030, 339600817518201684

Offset: 1

R. H. Hardin, Sep 26 2013

nonn

Column 4 of A229606.

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

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

Cf. A229606.

Empirical: a(n) = 27*a(n-1) - 288*a(n-2) + 1557*a(n-3) - 4644*a(n-4) + 8073*a(n-5) - 8343*a(n-6) + 5022*a(n-7) - 1620*a(n-8) + 216*a(n-9) for n > 11.

A229603 Number of defective 3-colorings of an n X 5 0..2 array connected horizontally and vertically with exactly two mistakes, and colors introduced in row-major 0..2 order.

Original entry on oeis.org

12, 925, 20714, 362100, 5655616, 82613904, 1153135492, 15568071652, 204858459714, 2641246065146, 33490766408662, 418803158565406, 5175912161534684, 63325575352273052, 768005500079367536

Offset: 1

R. H. Hardin, Sep 26 2013

nonn

Column 5 of A229606.

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

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

Cf. A229606.

Empirical: a(n) = 47*a(n-1) - 915*a(n-2) + 9649*a(n-3) - 60959*a(n-4) + 242397*a(n-5) - 616481*a(n-6) + 977203*a(n-7) - 836412*a(n-8) + 41816*a(n-9) + 793688*a(n-10) - 1000320*a(n-11) + 656832*a(n-12) - 262080*a(n-13) + 63744*a(n-14) - 8704*a(n-15) + 512*a(n-16) for n > 17.

A229604 Number of defective 3-colorings of an n X 6 0..2 array connected horizontally and vertically with exactly two mistakes, and colors introduced in row-major 0..2 order.

Original entry on oeis.org

40, 3924, 131345, 3476928, 82613904, 1840258874, 39229935270, 809714005005, 16301446350838, 321725691680589, 6247090415396847, 119665707667897987, 2265983192057928009, 42485559978048128856, 789743391503380249568

Offset: 1

R. H. Hardin, Sep 26 2013

nonn

Column 6 of A229606.

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

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

Cf. A229606.

Empirical: a(n) = 90*a(n-1) - 3573*a(n-2) + 83214*a(n-3) - 1278486*a(n-4) + 13836015*a(n-5) - 110021385*a(n-6) + 661896144*a(n-7) - 3076398702*a(n-8) + 11214272853*a(n-9) - 32398609896*a(n-10) + 74677395474*a(n-11) - 137758028106*a(n-12) + 203308881255*a(n-13) - 239066083215*a(n-14) + 222060410955*a(n-15) - 160604595216*a(n-16) + 88409012652*a(n-17) - 35729023024*a(n-18) + 9979813584*a(n-19) - 1718948736*a(n-20) + 137388096*a(n-21) for n > 23.

A229605 Number of defective 3-colorings of an n X 7 0..2 array connected horizontally and vertically with exactly two mistakes, and colors introduced in row-major 0..2 order.

Original entry on oeis.org

120, 15795, 792929, 31848813, 1153135492, 39229935270, 1279020266434, 40413033646242, 1246326317951687, 37697561397216125, 1122224822297521683, 32965710304040001780, 957481537679788357971, 27540249663372893582723

Offset: 1

R. H. Hardin, Sep 26 2013

nonn

Column 7 of A229606.

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 46

Cf. A229606.

Empirical recurrence of order 46 (see link above).

A229599 Number of defective 3-colorings of an n X n 0..2 array connected horizontally and vertically with exactly two mistakes, and colors introduced in row-major 0..2 order.

Original entry on oeis.org

0, 6, 396, 35182, 5655616, 1840258874, 1279020266434, 1956482857537638, 6709261067536603464, 52210936089708881164828, 929873887535519786302080272, 38136664055521875662056947040494

Offset: 1

R. H. Hardin, Sep 26 2013

nonn

Diagonal of A229606.

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

Cf. A229606.

cp's OEIS Frontend

A229600 Number of defective 3-colorings of an n X 2 0..2 array connected horizontally and vertically with exactly two mistakes, and colors introduced in row-major 0..2 order.

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A229601 Number of defective 3-colorings of an n X 3 0..2 array connected horizontally and vertically with exactly two mistakes, and colors introduced in row-major 0..2 order.

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A229602 Number of defective 3-colorings of an n X 4 0..2 array connected horizontally and vertically with exactly two mistakes, and colors introduced in row-major 0..2 order.

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A229603 Number of defective 3-colorings of an n X 5 0..2 array connected horizontally and vertically with exactly two mistakes, and colors introduced in row-major 0..2 order.

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A229604 Number of defective 3-colorings of an n X 6 0..2 array connected horizontally and vertically with exactly two mistakes, and colors introduced in row-major 0..2 order.

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A229605 Number of defective 3-colorings of an n X 7 0..2 array connected horizontally and vertically with exactly two mistakes, and colors introduced in row-major 0..2 order.

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A229599 Number of defective 3-colorings of an n X n 0..2 array connected horizontally and vertically with exactly two mistakes, and colors introduced in row-major 0..2 order.

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