A204705 -id:A204705 - cp's OEIS frontend

A204699 Number of n X 2 0..2 arrays with no occurrence of three equal elements in a row horizontally, vertically or nw-to-se diagonally, and new values 0..2 introduced in row major order.

2, 14, 96, 726, 5400, 40344, 301056, 2247264, 16773504, 125199744, 934502400, 6975223296, 52063770624, 388609284096, 2900619165696, 21650516238336, 161601653145600, 1206211160408064, 9003282670288896, 67201416721465344

Offset: 1

R. H. Hardin, Jan 18 2012

nonn

Column 2 of A204705.

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

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

Cf. A204705.

Empirical: a(n) = 6*a(n-1) + 12*a(n-2) - 8*a(n-3) for n>5.

Empirical g.f.: 2*x*(1 - 2*x)*(1 + 3*x - x^3) / ((1 + 2*x)*(1 - 8*x + 4*x^2)). - Colin Barker, Feb 23 2018

A204700 Number of nX3 0..2 arrays with no occurrence of three equal elements in a row horizontally, vertically or nw-to-se diagonally, and new values 0..2 introduced in row major order.

Original entry on oeis.org

4, 96, 1417, 22869, 362020, 5767683, 91733605, 1459710274, 23224443905, 369522237415, 5879375305236, 93545539546075, 1488382733670257, 23681339437114202, 376788704103588493, 5995004229216188035

Offset: 1

R. H. Hardin Jan 18 2012

nonn

Column 3 of A204705

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

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

Empirical: a(n) = 9*a(n-1) +117*a(n-2) -24*a(n-3) -1482*a(n-4) +884*a(n-5) +6805*a(n-6) -7217*a(n-7) +875*a(n-8) -9444*a(n-9) +23926*a(n-10) -157560*a(n-11) +235676*a(n-12) +268960*a(n-13) -735296*a(n-14) +199456*a(n-15) +747264*a(n-16) -760384*a(n-17) -340800*a(n-18) +784192*a(n-19) -38208*a(n-20) -346880*a(n-21) +138880*a(n-22) +50176*a(n-23) -91904*a(n-24) +17408*a(n-25) +25600*a(n-26) -8192*a(n-27) -4096*a(n-28) for n>31

A204701 Number of nX4 0..2 arrays with no occurrence of three equal elements in a row horizontally, vertically or nw-to-se diagonally, and new values 0..2 introduced in row major order.

Original entry on oeis.org

11, 726, 22869, 835135, 29846373, 1074195735, 38585324821, 1386815731346, 49835668719324, 1790952554181415, 64360800888516224, 2312920275315600518, 83118816237627091277, 2987020411865810161864, 107343805323748931471929

Offset: 1

R. H. Hardin Jan 18 2012

nonn

Column 4 of A204705

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

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

A204702 Number of nX5 0..2 arrays with no occurrence of three equal elements in a row horizontally, vertically or nw-to-se diagonally, and new values 0..2 introduced in row major order.

Original entry on oeis.org

30, 5400, 362020, 29846373, 2389914827, 192759130113, 15521787839696, 1250634888842984, 100749784360671667, 8116764740949394264, 653904134820543785397, 52680223968250151357189, 4244049256144093743987455

Offset: 1

R. H. Hardin Jan 18 2012

nonn

Column 5 of A204705

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

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

A204703 Number of nX6 0..2 arrays with no occurrence of three equal elements in a row horizontally, vertically or nw-to-se diagonally, and new values 0..2 introduced in row major order.

Original entry on oeis.org

82, 40344, 5767683, 1074195735, 192759130113, 34925753412578, 6319625580942184, 1144097011453760287, 207096410275997210933, 37489155843579834602268, 6786272895764958062549631

Offset: 1

R. H. Hardin Jan 18 2012

nonn

Column 6 of A204705

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

R. H. Hardin, Table of n, a(n) for n = 1..47

A204698 Number of n X n 0..2 arrays with no occurrence of three equal elements in a row horizontally, vertically or nw-to-se diagonally, and new values 0..2 introduced in row major order.

Original entry on oeis.org

1, 14, 1417, 835135, 2389914827, 34925753412578, 2568926644225402978, 954699753721419299486986

Offset: 1

R. H. Hardin Jan 18 2012

nonn

Diagonal of A204705

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

A204704 Number of nX7 0..2 arrays with no occurrence of three equal elements in a row horizontally, vertically or nw-to-se diagonally, and new values 0..2 introduced in row major order.

Original entry on oeis.org

224, 301056, 91733605, 38585324821, 15521787839696, 6319625580942184, 2568926644225402978, 1044792211767082026764, 424880469013125627760792, 172792044105478879279518350, 70270849522277745874734015748

Offset: 1

R. H. Hardin Jan 18 2012

nonn

Column 7 of A204705

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

cp's OEIS Frontend

A204699 Number of n X 2 0..2 arrays with no occurrence of three equal elements in a row horizontally, vertically or nw-to-se diagonally, and new values 0..2 introduced in row major order.

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A204700 Number of nX3 0..2 arrays with no occurrence of three equal elements in a row horizontally, vertically or nw-to-se diagonally, and new values 0..2 introduced in row major order.

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A204701 Number of nX4 0..2 arrays with no occurrence of three equal elements in a row horizontally, vertically or nw-to-se diagonally, and new values 0..2 introduced in row major order.

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A204702 Number of nX5 0..2 arrays with no occurrence of three equal elements in a row horizontally, vertically or nw-to-se diagonally, and new values 0..2 introduced in row major order.

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A204703 Number of nX6 0..2 arrays with no occurrence of three equal elements in a row horizontally, vertically or nw-to-se diagonally, and new values 0..2 introduced in row major order.

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A204698 Number of n X n 0..2 arrays with no occurrence of three equal elements in a row horizontally, vertically or nw-to-se diagonally, and new values 0..2 introduced in row major order.

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A204704 Number of nX7 0..2 arrays with no occurrence of three equal elements in a row horizontally, vertically or nw-to-se diagonally, and new values 0..2 introduced in row major order.

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