A229694 -id:A229694 - cp's OEIS frontend

A229689 Number of defective 3-colorings of an n X 3 0..2 array connected horizontally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

1, 43, 626, 6732, 62856, 539568, 4377888, 34105536, 257634432, 1899645696, 13735899648, 97733495808, 686049232896, 4760622968832, 32708331380736, 222789318524928, 1506002505596928, 10111798278291456, 67486591206162432

Offset: 1

R. H. Hardin, Sep 27 2013

nonn

Column 3 of A229694.

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

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

Cf. A229694.

Empirical: a(n) = 18*a(n-1) -108*a(n-2) +216*a(n-3) for n > 4.

Empirical: g.f. x -x^2*(43-148*x+108*x^2) / (6*x-1)^3. - R. J. Mathar, Sep 29 2013

A229690 Number of defective 3-colorings of an nX4 0..2 array connected horizontally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

Original entry on oeis.org

3, 245, 5077, 80757, 1125333, 14461173, 175867605, 2054728053, 23284024533, 257577229557, 2794463987157, 29833314755445, 314218549864917, 3271569607417077, 33725758239805653, 344669380723927413

Offset: 1

R. H. Hardin, Sep 27 2013

nonn

Column 4 of A229694

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

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

Empirical: a(n) = 27*a(n-1) -243*a(n-2) +729*a(n-3) for n>4.

Empirical: g.f. 3*x-x^2*(245-1538*x+3213*x^2) / (9*x-1)^3. - R. J. Mathar, Sep 29 2013

A229691 Number of defective 3-colorings of an nX5 0..2 array connected horizontally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

Original entry on oeis.org

12, 1171, 35825, 848937, 17724789, 342532665, 6279934941, 110801828529, 1898544262293, 31786996628745, 522316663574733, 8450380115641377, 134940473888031045, 2130891564532483449, 33326706458497564413

Offset: 1

R. H. Hardin, Sep 27 2013

nonn

Column 5 of A229694

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

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

Empirical: a(n) = 45*a(n-1) -729*a(n-2) +4995*a(n-3) -13122*a(n-4) +14580*a(n-5) -5832*a(n-6) for n>7.

Empirical: 12*x -x^2*(-1171+16870*x-90471*x^2+210096*x^3-212220*x^4+81648*x^5) / (18*x^2-15*x+1)^3. - R. J. Mathar, Sep 29 2013

A229692 Number of defective 3-colorings of an n X 6 0..2 array connected horizontally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

Original entry on oeis.org

40, 5077, 230383, 8186713, 258006388, 7551515197, 210095323918, 5632122625852, 146747625919741, 3738362679893995, 93505337317628617, 2303524911169269100, 56025377123719298929, 1347778566401139093298, 32117071054579505478784

Offset: 1

R. H. Hardin, Sep 27 2013

nonn

Column 6 of A229694.

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

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

Empirical: a(n) = 75*a(n-1) - 2145*a(n-2) + 29368*a(n-3) - 205200*a(n-4) + 803115*a(n-5) - 1842183*a(n-6) + 2460375*a(n-7) - 1771470*a(n-8) + 531441*a(n-9) for n > 11.

A229693 Number of defective 3-colorings of an n X 7 0..2 array connected horizontally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

Original entry on oeis.org

120, 20691, 1400413, 75035643, 3583403667, 159377253183, 6749642728251, 275739382892979, 10957241965280031, 425954258229381831, 16265054107660003947, 611918047133484899067, 22734198484723715670855

Offset: 1

R. H. Hardin, Sep 27 2013

nonn

Column 7 of A229694.

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

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

Empirical: a(n) = 126*a(n-1) - 6345*a(n-2) + 165456*a(n-3) - 2474469*a(n-4) + 22918302*a(n-5) - 138045627*a(n-6) + 554666940*a(n-7) - 1494608922*a(n-8) + 2659094568*a(n-9) - 2986698420*a(n-10) + 1913187600*a(n-11) - 531441000*a(n-12) for n > 14.

A229695 Number of defective 3-colorings of a 2Xn 0..2 array connected horizontally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

Original entry on oeis.org

0, 3, 43, 245, 1171, 5077, 20691, 80757, 305235, 1125333, 4067091, 14461173, 50723091, 175867605, 603736659, 2054728053, 6940088019, 23284024533, 77651501715, 257577229557, 850273182099, 2794463987157, 9147385165779

Offset: 1

R. H. Hardin, Sep 27 2013

nonn

Row 2 of A229694

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

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

Empirical: a(n) = 9*a(n-1) -27*a(n-2) +27*a(n-3) for n>6.

Empirical: G.f. 3*x^2+43*x^3 -x^4*(245-1034*x+1153*x^2) / (3*x-1)^3. - R. J. Mathar, Sep 29 2013

A229696 Number of defective 3-colorings of a 3 X n 0..2 array connected horizontally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

Original entry on oeis.org

0, 40, 626, 5077, 35825, 230383, 1400413, 8184819, 46455457, 257724695, 1403839397, 7532391243, 39908047865, 209177764015, 1086276818845, 5595663437379, 28620024582289, 145460267764487, 735134318022101

Offset: 1

R. H. Hardin, Sep 27 2013

nonn

Row 3 of A229694.

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

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 > 10.

A229697 Number of defective 3-colorings of a 4 X n 0..2 array connected horizontally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

Original entry on oeis.org

0, 336, 6732, 80757, 848937, 8186713, 75035643, 663220698, 5704874295, 48038840103, 397625913450, 3244798314423, 26164241721531, 208829737022022, 1652110212078675, 12969730076956551, 101126149198462638

Offset: 1

R. H. Hardin, Sep 27 2013

nonn

Row 4 of A229694.

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

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

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 > 17.

A229698 Number of defective 3-colorings of a 5 X n 0..2 array connected horizontally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

Original entry on oeis.org

0, 2304, 62856, 1125333, 17724789, 258006388, 3583403667, 48115029568, 629879095575, 8082470014816, 102040738816275, 1270988929203520, 15651508367076687, 190863964416217648, 2307849686574725259

Offset: 1

R. H. Hardin, Sep 27 2013

nonn

Row 5 of A229694.

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

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

Empirical: a(n) = 48*a(n-1) - 960*a(n-2) + 10468*a(n-3) - 68685*a(n-4) + 282276*a(n-5) - 718624*a(n-6) + 997536*a(n-7) - 166467*a(n-8) - 2005784*a(n-9) + 3520224*a(n-10) - 1956780*a(n-11) - 1660207*a(n-12) + 3547332*a(n-13) - 2236608*a(n-14) - 28632*a(n-15) + 1014720*a(n-16) - 774528*a(n-17) + 307392*a(n-18) - 71424*a(n-19) + 9216*a(n-20) - 512*a(n-21) for n > 27.

A229699 Number of defective 3-colorings of a 6 X n 0..2 array connected horizontally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

Original entry on oeis.org

0, 14080, 539568, 14461173, 342532665, 7551515197, 159377253183, 3259483737876, 65096269054893, 1275742582477605, 24619023091178172, 469011723417138726, 8837860575136215933, 164977425368113931622, 3054546692947278299664

Offset: 1

R. H. Hardin, Sep 27 2013

nonn

Row 6 of A229694.

			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
  0 2 1   0 2 0   0 1 2   0 1 1   0 2 1   0 1 0   0 1 0
  1 0 2   1 2 0   1 0 1   1 2 0   1 1 2   1 0 2   0 2 1
  1 0 1   1 2 2   2 0 1   1 2 0   0 1 2   2 1 0   1 2 1
  1 2 1   0 1 2   1 2 2   0 1 2   0 1 0   0 1 2   0 2 1
  2 1 0   1 0 2   0 1 2   2 0 2   0 1 2   2 0 1   2 0 0

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

Cf. A229694.

Empirical: a(n) = 93*a(n-1) - 3821*a(n-2) + 91881*a(n-3) - 1443186*a(n-4) + 15597045*a(n-5) - 117977554*a(n-6) + 609544785*a(n-7) - 1876860224*a(n-8) + 672776487*a(n-9) + 25778362941*a(n-10) - 141476097204*a(n-11) + 370797282552*a(n-12) - 240042337335*a(n-13) - 2043251213592*a(n-14) + 9124472514798*a(n-15) - 19258050947535*a(n-16) + 16290852033186*a(n-17) + 33202946615828*a(n-18) - 157802120078712*a(n-19) + 340033091646544*a(n-20) - 501365137481568*a(n-21) + 551133229309632*a(n-22) - 463504649118336*a(n-23) + 298842654582272*a(n-24) - 145678126101504*a(n-25) + 52056403136512*a(n-26) - 12877220044800*a(n-27) + 1971231621120*a(n-28) - 140685410304*a(n-29) for n > 39.

cp's OEIS Frontend

A229689 Number of defective 3-colorings of an n X 3 0..2 array connected horizontally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

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A229690 Number of defective 3-colorings of an nX4 0..2 array connected horizontally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

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A229691 Number of defective 3-colorings of an nX5 0..2 array connected horizontally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

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A229692 Number of defective 3-colorings of an n X 6 0..2 array connected horizontally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

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A229693 Number of defective 3-colorings of an n X 7 0..2 array connected horizontally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

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A229695 Number of defective 3-colorings of a 2Xn 0..2 array connected horizontally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

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A229696 Number of defective 3-colorings of a 3 X n 0..2 array connected horizontally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

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A229697 Number of defective 3-colorings of a 4 X n 0..2 array connected horizontally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

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A229698 Number of defective 3-colorings of a 5 X n 0..2 array connected horizontally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

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A229699 Number of defective 3-colorings of a 6 X n 0..2 array connected horizontally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

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