A221828 -id:A221828 - cp's OEIS frontend

A221825 Number of nX3 arrays of occupancy after each element moves to some horizontal, vertical or antidiagonal neighbor, without 2-loops or left turns.

0, 16, 202, 2930, 41618, 592601, 8434490, 120053263, 1708776751, 24321871624, 346185271087, 4927426856495, 70134512879660, 998259343308353, 14208720864088015, 202239778618252032, 2878579180120974241

Offset: 1

R. H. Hardin Jan 26 2013

nonn

Column 3 of A221828

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

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

Empirical: a(n) = 17*a(n-1) -39*a(n-2) -14*a(n-3) +134*a(n-4) -161*a(n-5) +50*a(n-6) -147*a(n-7) +129*a(n-8) +215*a(n-9) -131*a(n-10) +53*a(n-11) -92*a(n-12) -97*a(n-13) +31*a(n-14) -27*a(n-15) +16*a(n-16) +6*a(n-17)

A221826 Number of nX4 arrays of occupancy after each element moves to some horizontal, vertical or antidiagonal neighbor, without 2-loops or left turns.

Original entry on oeis.org

0, 73, 2879, 115417, 4755445, 194407111, 7954432829, 325446165881, 13315083231576, 544765825231628, 22288229643043523, 911887582567144091, 37308434607556030347, 1526415443763878545790, 62450867501566841285468

Offset: 1

R. H. Hardin Jan 26 2013

nonn

Column 4 of A221828

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

R. H. Hardin, Table of n, a(n) for n = 1..46

A221829 Number of 2 X n arrays of occupancy after each element moves to some horizontal, vertical or antidiagonal neighbor, without 2-loops or left turns.

Original entry on oeis.org

0, 3, 16, 73, 333, 1519, 6929, 31607, 144177, 657671, 3000001, 13684663, 62423313, 284747239, 1298889569, 5924953367, 27026987697, 123285031751, 562371183361, 2565285853303, 11701686899793, 53377862792359, 243485940162209

Offset: 1

R. H. Hardin, Jan 26 2013

nonn

Row 2 of A221828.

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

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

Cf. A221828.

Empirical: a(n) = 5*a(n-1) - 2*a(n-2) for n>4.
Conjectures from Colin Barker, Aug 11 2018: (Start)
G.f.: x^2*(3 + x - x^2) / (1 - 5*x + 2*x^2).
a(n) = (2^(-4-n)*((5-sqrt(17))^n*(-7+sqrt(17)) + (5+sqrt(17))^n*(7+sqrt(17)))) / sqrt(17) for n>2.
(End)

A221830 Number of 3Xn arrays of occupancy after each element moves to some horizontal, vertical or antidiagonal neighbor, without 2-loops or left turns.

Original entry on oeis.org

0, 14, 202, 2879, 40983, 583419, 8304016, 118195328, 1682332699, 23945477164, 340827864824, 4851172222091, 69049142818994, 982810732310121, 13988833113623959, 199110007092542464, 2834031588079597413

Offset: 1

R. H. Hardin Jan 26 2013

nonn

Row 3 of A221828

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

R. H. Hardin, Table of n, a(n) for n = 1..184

Empirical: a(n) = 17*a(n-1) -39*a(n-2) -14*a(n-3) +134*a(n-4) -161*a(n-5) +50*a(n-6) -147*a(n-7) +129*a(n-8) +215*a(n-9) -131*a(n-10) +53*a(n-11) -92*a(n-12) -97*a(n-13) +31*a(n-14) -27*a(n-15) +16*a(n-16) +6*a(n-17) for n>18

A221831 Number of 4Xn arrays of occupancy after each element moves to some horizontal, vertical or antidiagonal neighbor, without 2-loops or left turns.

Original entry on oeis.org

0, 64, 2930, 115417, 4715043, 192788993, 7888216533, 322723834959, 13203608881221, 540203150208573, 22101534579211095, 904249026745794715, 36995912673327194833, 1513629078095632460534, 61927733346071816062294

Offset: 1

R. H. Hardin Jan 26 2013

nonn

Row 4 of A221828

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

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

A221827 Number of nX5 arrays of occupancy after each element moves to some horizontal, vertical or antidiagonal neighbor, without 2-loops or left turns.

Original entry on oeis.org

0, 333, 40983, 4715043, 570066685, 68489860450, 8224749361083, 987885812260577, 118641972922938733, 14248324215718943851, 1711142647446159966808

Offset: 1

R. H. Hardin Jan 26 2013

nonn

Column 5 of A221828

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

A221832 Number of 5 X n arrays of occupancy after each element moves to some horizontal, vertical or antidiagonal neighbor, without 2-loops or left turns.

Original entry on oeis.org

0, 292, 41618, 4755445, 570066685, 68573607669, 8233561918895, 988927665068644, 118765199887208210

Offset: 1

R. H. Hardin, Jan 26 2013

nonn

Row 5 of A221828.

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

Cf. A221828.

cp's OEIS Frontend

A221825 Number of nX3 arrays of occupancy after each element moves to some horizontal, vertical or antidiagonal neighbor, without 2-loops or left turns.

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A221826 Number of nX4 arrays of occupancy after each element moves to some horizontal, vertical or antidiagonal neighbor, without 2-loops or left turns.

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A221829 Number of 2 X n arrays of occupancy after each element moves to some horizontal, vertical or antidiagonal neighbor, without 2-loops or left turns.

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A221830 Number of 3Xn arrays of occupancy after each element moves to some horizontal, vertical or antidiagonal neighbor, without 2-loops or left turns.

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A221831 Number of 4Xn arrays of occupancy after each element moves to some horizontal, vertical or antidiagonal neighbor, without 2-loops or left turns.

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A221827 Number of nX5 arrays of occupancy after each element moves to some horizontal, vertical or antidiagonal neighbor, without 2-loops or left turns.

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A221832 Number of 5 X n arrays of occupancy after each element moves to some horizontal, vertical or antidiagonal neighbor, without 2-loops or left turns.

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