A221693 -id:A221693 - cp's OEIS frontend

A221689 Number of n X 3 arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without consecutive moves in the same direction.

6, 152, 3112, 63676, 1302720, 26650988, 545221260, 11154026300, 228186749552, 4668196767064, 95500991265668, 1953739262283024, 39969188300499044, 817681276128120100, 16727952148700884996, 342216938625170086928

Offset: 1

R. H. Hardin, Jan 22 2013

nonn

Column 3 of A221693.

			Some solutions for n=3:
..0..4..0....0..3..0....0..2..1....0..2..2....0..3..1....1..1..1....1..2..0
..1..0..0....1..1..0....0..1..0....0..1..0....0..1..0....1..1..0....1..2..1
..1..1..2....2..2..0....2..1..2....1..1..2....2..1..1....0..4..0....0..2..0

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

Cf. A221693.

Empirical: a(n) = 24*a(n-1) - 69*a(n-2) - 71*a(n-3) + 2*a(n-4) for n>5.

Empirical g.f.: 2*x*(3 + 4*x - 61*x^2 - 49*x^3 + 2*x^4) / (1 - 24*x + 69*x^2 + 71*x^3 - 2*x^4). - Colin Barker, Aug 10 2018

A221690 Number of nX4 arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without consecutive moves in the same direction.

Original entry on oeis.org

13, 1336, 95076, 7033429, 520770016, 38558774282, 2854945130275, 211383822013331, 15651127479431664, 1158829375610866111, 85801199678309146886, 6352829859620504245102, 470371595862197876296617

Offset: 1

R. H. Hardin Jan 22 2013

nonn

Column 4 of A221693

			Some solutions for n=3
..0..3..1..0....1..0..2..1....2..1..0..1....0..1..2..0....2..0..1..1
..0..0..4..2....1..0..0..3....0..2..2..2....3..1..1..2....0..2..0..3
..1..0..1..0....1..2..1..0....0..0..0..2....0..0..2..0....2..0..0..1

R. H. Hardin, Table of n, a(n) for n = 1..78

A221691 Number of nX5 arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without consecutive moves in the same direction.

Original entry on oeis.org

28, 11036, 2627760, 659020617, 164441398718, 41023076707062, 10233875156794211, 2553004334803146133, 636887763097823284411, 158881831138559422724173, 39635611567879464460692735

Offset: 1

R. H. Hardin Jan 22 2013

nonn

Column 5 of A221693

			Some solutions for n=3
..0..2..2..0..1....0..2..0..0..2....0..2..0..2..0....0..3..1..2..0
..0..4..0..0..1....0..4..0..0..1....0..3..0..3..0....0..2..0..1..1
..0..1..1..2..1....0..3..0..3..0....0..0..2..1..2....0..2..0..3..0

R. H. Hardin, Table of n, a(n) for n = 1..17

A221692 Number of nX6 arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without consecutive moves in the same direction.

Original entry on oeis.org

60, 92660, 74531185, 64509677154, 55433846144035, 47681199145323119, 41016076097898190730, 35282822653645381320038, 30350969754572497969358415, 26108492570724327368100591178, 22459031054635514974048155933027

Offset: 1

R. H. Hardin Jan 22 2013

nonn

Column 6 of A221693

			Some solutions for n=3
..0..1..0..2..1..2....0..1..0..1..1..0....0..1..0..1..2..0....0..1..0..2..1..1
..1..1..0..0..1..1....1..1..3..1..1..0....1..1..3..1..1..0....1..1..1..1..0..1
..1..4..0..0..3..0....1..2..1..3..0..1....1..1..1..0..3..1....1..1..2..1..1..2

R. H. Hardin, Table of n, a(n) for n = 1..25

A221694 Number of 2 X n arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without consecutive moves in the same direction.

Original entry on oeis.org

1, 21, 152, 1336, 11036, 92660, 774380, 6479664, 54200980, 453418640, 3792991120, 31729761276, 265430689860, 2220422566716, 18574626389432, 155383375746468, 1299837358873328, 10873603138412824, 90961568659281764, 760925966163564220

Offset: 1

R. H. Hardin, Jan 22 2013

nonn

Row 2 of A221693.

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

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

Cf. A221693.

Empirical: a(n) = 5*a(n-1) + 28*a(n-2) + 9*a(n-3) - 62*a(n-4) - 30*a(n-5) + 64*a(n-6) + 32*a(n-7) - 32*a(n-8) + 32*a(n-9).

Empirical g.f.: x*(1 + 16*x + 19*x^2 - 21*x^3 - 27*x^4 + 36*x^5 + 38*x^6 - 24*x^7 + 24*x^8) / ((1 + 2*x)^2*(1 - 9*x + 4*x^2 + 11*x^3 + 2*x^4 - 22*x^5 + 16*x^6 - 8*x^7)). - Colin Barker, Aug 10 2018

A221695 Number of 3Xn arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without consecutive moves in the same direction.

Original entry on oeis.org

1, 144, 3112, 95076, 2627760, 74531185, 2098932856, 59210733473, 1669668324450, 47086135048676, 1327854674388881, 37446255355092156, 1056006037475086696, 29779973215497145163, 839812326958816104725, 23683188619380401285537

Offset: 1

R. H. Hardin Jan 22 2013

nonn

Row 3 of A221693

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

R. H. Hardin, Table of n, a(n) for n = 1..69

A221696 Number of 4Xn arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without consecutive moves in the same direction.

Original entry on oeis.org

1, 987, 63676, 7033429, 659020617, 64509677154, 6233675847228, 604346923784252, 58538232535028520, 5671250113728678882, 549411330594167686392, 53225495837252796349285, 5156336905625087231654148

Offset: 1

R. H. Hardin Jan 22 2013

nonn

Row 4 of A221693

			Some solutions for n=3
..2..0..0....2..0..1....0..1..1....1..0..0....0..4..1....1..0..0....0..3..2
..0..3..1....1..1..0....2..3..0....1..4..0....0..0..1....2..2..1....0..0..1
..1..0..1....2..0..0....0..0..0....2..0..2....2..1..0....0..2..0....1..2..1
..1..3..0....1..3..1....2..1..2....0..1..1....0..3..0....1..3..0....1..0..1

R. H. Hardin, Table of n, a(n) for n = 1..18

cp's OEIS Frontend

A221689 Number of n X 3 arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without consecutive moves in the same direction.

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A221690 Number of nX4 arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without consecutive moves in the same direction.

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A221691 Number of nX5 arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without consecutive moves in the same direction.

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A221692 Number of nX6 arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without consecutive moves in the same direction.

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A221694 Number of 2 X n arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without consecutive moves in the same direction.

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A221695 Number of 3Xn arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without consecutive moves in the same direction.

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A221696 Number of 4Xn arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without consecutive moves in the same direction.

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