A229637 -id:A229637 - cp's OEIS frontend

A229632 Number of defective 3-colorings of an nX3 0..2 array connected horizontally, diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

1, 40, 244, 1496, 8800, 50084, 277996, 1513104, 8106632, 42869740, 224232436, 1161920760, 5972173872, 30479422388, 154582269500, 779632820512, 3912450838808, 19545592617532, 97246103407556, 482032538140680

Offset: 1

R. H. Hardin, Sep 27 2013

nonn

Column 3 of A229637

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

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

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 -4*x^2*(2*x-5)*(12*x^4-45*x^3+47*x^2-17*x+2) / (2*x^2-5*x+1)^3. - R. J. Mathar, Sep 29 2013

A229633 Number of defective 3-colorings of an n X 4 0..2 array connected horizontally, diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

Original entry on oeis.org

3, 122, 1109, 10227, 89331, 747299, 6049298, 47723226, 368769958, 2801445986, 20980532622, 155235487082, 1136689596246, 8248224017298, 59378458285438, 424468785559258, 3015393888558342, 21301249097825858, 149716107860461294

Offset: 1

R. H. Hardin, Sep 27 2013

nonn

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

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

Column 4 of A229637.

Empirical: a(n) = 21*a(n-1) - 159*a(n-2) + 511*a(n-3) - 636*a(n-4) + 336*a(n-5) - 64*a(n-6) for n>9.

Empirical g.f.: x*(3 + 59*x - 976*x^2 + 4803*x^3 - 9539*x^4 + 7326*x^5 - 1825*x^6 - 76*x^7 + 25*x^8) / (1 - 7*x + 4*x^2)^3. - Colin Barker, Sep 20 2018

A229634 Number of defective 3-colorings of an n X 5 0..2 array connected horizontally, diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

Original entry on oeis.org

12, 488, 6031, 77620, 960325, 11485716, 133784624, 1525870912, 17108056051, 189113977298, 2065634425127, 22332806237194, 239326746885334, 2544956244990312, 26878587507519977, 282161860575964390

Offset: 1

R. H. Hardin, Sep 27 2013

nonn

Column 5 of A229637.

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

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

Cf. A229637.

Empirical: a(n) = 42*a(n-1) - 723*a(n-2) + 6569*a(n-3) - 33687*a(n-4) + 94839*a(n-5) - 116010*a(n-6) - 55215*a(n-7) + 305043*a(n-8) - 230994*a(n-9) - 118011*a(n-10) + 243513*a(n-11) - 84933*a(n-12) - 40719*a(n-13) + 42804*a(n-14) - 14887*a(n-15) + 2598*a(n-16) - 228*a(n-17) + 8*a(n-18) for n > 20.

A229635 Number of defective 3-colorings of an n X 6 0..2 array connected horizontally, diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

Original entry on oeis.org

40, 1608, 28448, 535671, 9722206, 170405645, 2902520386, 48303362606, 788657935296, 12673198849045, 200926746561814, 3149086238797127, 48865266229013882, 751678393470169836, 11474405764402402524

Offset: 1

R. H. Hardin, Sep 27 2013

nonn

Column 6 of A229637.

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

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

Empirical: a(n) = 54*a(n-1) - 1140*a(n-2) + 11637*a(n-3) - 54252*a(n-4) + 33192*a(n-5) + 658756*a(n-6) - 1921212*a(n-7) - 1566516*a(n-8) + 12850374*a(n-9) - 7108644*a(n-10) - 35018232*a(n-11) + 43506046*a(n-12) + 38500440*a(n-13) - 85687812*a(n-14) - 200796*a(n-15) + 75241308*a(n-16) - 31685592*a(n-17) - 25769200*a(n-18) + 20878068*a(n-19) + 213348*a(n-20) - 3655770*a(n-21) + 608916*a(n-22) + 230904*a(n-23) - 61761*a(n-24) - 2790*a(n-25) + 1800*a(n-26) - 125*a(n-27) for n > 30.

A229636 Number of defective 3-colorings of an n X 7 0..2 array connected horizontally, diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

Original entry on oeis.org

120, 5392, 136778, 3723370, 98015235, 2495874984, 61836040854, 1498317588826, 35650331594818, 835527599342816, 19334282699326025, 442561024351155220, 10035487974561746994, 225705889177614527760, 5039777091823275662663

Offset: 1

R. H. Hardin, Sep 27 2013

nonn

Column 7 of A229637.

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 57

Empirical recurrence of order 57 (see link above).

A229638 Number of defective 3-colorings of a 2 X n 0..2 array connected horizontally, diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

Original entry on oeis.org

0, 6, 40, 122, 488, 1608, 5392, 17368, 55232, 172896, 535296, 1641376, 4992896, 15083648, 45297408, 135323008, 402405376, 1191699968, 3516119040, 10339711488, 30313351168, 88624646144, 258445856768, 751910639616, 2182836600832

Offset: 1

R. H. Hardin, Sep 27 2013

nonn

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

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

Row 2 of A229637.

Empirical: a(n) = 6*a(n-1) - 6*a(n-2) - 16*a(n-3) + 12*a(n-4) + 24*a(n-5) + 8*a(n-6).

Empirical g.f.: 2*x^2*(1 - x)*(3 + 5*x - 36*x^2 + 10*x^3) / (1 - 2*x - 2*x^2)^3. - Colin Barker, Sep 20 2018

A229639 Number of defective 3-colorings of a 3 X n 0..2 array connected horizontally, diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

Original entry on oeis.org

0, 39, 244, 1109, 6031, 28448, 136778, 633328, 2905016, 13118016, 58633648, 259523840, 1139461984, 4967050352, 21516000592, 92679568016, 397212173264, 1694694809008, 7200709256752, 30481238674128, 128588345884944

Offset: 1

R. H. Hardin, Sep 27 2013

nonn

Row 3 of A229637.

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

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

Empirical: a(n) = 9*a(n-1) - 15*a(n-2) - 51*a(n-3) + 96*a(n-4) + 138*a(n-5) - 92*a(n-6) - 60*a(n-7) +4 8*a(n-8) - 8*a(n-9) for n > 12.

A229640 Number of defective 3-colorings of a 4 X n 0..2 array connected horizontally, diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

Original entry on oeis.org

0, 202, 1496, 10227, 77620, 535671, 3723370, 25022190, 166505166, 1090285513, 7066637900, 45333775056, 288422981684, 1821192582307, 11424271291526, 71241698297248, 441922120307156, 2728236364222397, 16770150954151850

Offset: 1

R. H. Hardin, Sep 27 2013

nonn

Row 4 of A229637.

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

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

Empirical: a(n) = 9*a(n-1) + 21*a(n-2) - 270*a(n-3) - 357*a(n-4) + 2967*a(n-5) + 4906*a(n-6) - 10083*a(n-7) - 18957*a(n-8) + 15750*a(n-9) + 31293*a(n-10) - 13335*a(n-11) - 23929*a(n-12) + 6426*a(n-13) + 7824*a(n-14) - 1336*a(n-15) - 1152*a(n-16) + 96*a(n-17) + 64*a(n-18) for n > 21.

A229641 Number of defective 3-colorings of a 5 X n 0..2 array connected horizontally, diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

Original entry on oeis.org

0, 925, 8800, 89331, 960325, 9722206, 98015235, 960209886, 9295982009, 88583128280, 835152387679, 7790969750780, 72061578435025, 661325695334298, 6028108188010041, 54611818274641520, 492062341420006203

Offset: 1

R. H. Hardin, Sep 27 2013

nonn

Row 5 of A229637.

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

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

Empirical: a(n) = 18*a(n-1) - 15*a(n-2) - 1191*a(n-3) + 3468*a(n-4) + 31983*a(n-5) - 108707*a(n-6) - 424479*a(n-7) + 1614489*a(n-8) + 2851598*a(n-9) - 13478352*a(n-10) - 7797810*a(n-11) + 66347438*a(n-12) - 12632640*a(n-13) - 190067859*a(n-14) + 147888798*a(n-15) + 287096430*a(n-16) - 412178619*a(n-17) - 138135927*a(n-18) + 522690894*a(n-19) - 168525432*a(n-20) - 273411640*a(n-21) + 227616084*a(n-22) + 9610272*a(n-23) - 73617984*a(n-24) + 21460464*a(n-25) + 7359984*a(n-26) - 4611168*a(n-27) + 186624*a(n-28) + 279936*a(n-29) - 46656*a(n-30) for n > 33.

A229642 Number of defective 3-colorings of a 6 X n 0..2 array connected horizontally, diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

Original entry on oeis.org

0, 3924, 50084, 747299, 11485716, 170405645, 2495874984, 35693194243, 503332240292, 6990933433009, 96001895136772, 1304362116389856, 17565879194817688, 234673938451844201, 3113368949256998744

Offset: 1

R. H. Hardin, Sep 27 2013

nonn

Row 6 of A229637.

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 69

Empirical recurrence of order 69 (see link above).

cp's OEIS Frontend

A229632 Number of defective 3-colorings of an nX3 0..2 array connected horizontally, diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

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A229633 Number of defective 3-colorings of an n X 4 0..2 array connected horizontally, diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

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A229634 Number of defective 3-colorings of an n X 5 0..2 array connected horizontally, diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

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A229635 Number of defective 3-colorings of an n X 6 0..2 array connected horizontally, diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

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A229636 Number of defective 3-colorings of an n X 7 0..2 array connected horizontally, diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

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A229638 Number of defective 3-colorings of a 2 X n 0..2 array connected horizontally, diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

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A229639 Number of defective 3-colorings of a 3 X n 0..2 array connected horizontally, diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

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A229640 Number of defective 3-colorings of a 4 X n 0..2 array connected horizontally, diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

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A229641 Number of defective 3-colorings of a 5 X n 0..2 array connected horizontally, diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

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A229642 Number of defective 3-colorings of a 6 X n 0..2 array connected horizontally, diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

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