A221898 -id:A221898 - cp's OEIS frontend

A221894 Number of n X 2 arrays of occupancy after each element stays put or moves to some horizontal, vertical or antidiagonal neighbor, without move-in move-out straight through or left turns.

3, 31, 266, 2305, 19936, 172624, 1494152, 12933821, 111957318, 969123166, 8388906524, 72615905296, 628576515760, 5441072941952, 47098919537873, 407696835820987, 3529098152699791, 30548517126329090, 264433534642030465

Offset: 1

R. H. Hardin, Jan 30 2013

nonn

Column 2 of A221898.

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

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

Cf. A221898.

Empirical: a(n) = 5*a(n-1) + 26*a(n-2) + 45*a(n-3) + 34*a(n-4) - 2*a(n-5) - 4*a(n-6) + a(n-7).

Empirical g.f.: x*(3 + 16*x + 33*x^2 + 34*x^3 - 2*x^4 - 4*x^5 + x^6) / (1 - 5*x - 26*x^2 - 45*x^3 - 34*x^4 + 2*x^5 + 4*x^6 - x^7). - Colin Barker, Aug 11 2018

A221895 Number of nX3 arrays of occupancy after each element stays put or moves to some horizontal, vertical or antidiagonal neighbor, without move-in move-out straight through or left turns.

Original entry on oeis.org

6, 258, 7667, 235332, 7197649, 220361275, 6744533268, 206439650412, 6318757208626, 193406107213008, 5919823712888467, 181195475755599060, 5546077402982111186, 169755753751290765761, 5195927470447150844696

Offset: 1

R. H. Hardin Jan 30 2013

nonn

Column 3 of A221898

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

R. H. Hardin, Table of n, a(n) for n = 1..163

Empirical: a(n) = 14*a(n-1) +401*a(n-2) +3090*a(n-3) +7741*a(n-4) -40484*a(n-5) -361940*a(n-6) -1090743*a(n-7) -1171988*a(n-8) +2002414*a(n-9) +720120*a(n-10) -7394610*a(n-11) +17527526*a(n-12) -2069693*a(n-13) -44623518*a(n-14) +78779650*a(n-15) -104778098*a(n-16) +119555094*a(n-17) +11992813*a(n-18) -174397406*a(n-19) +103166505*a(n-20) +131329969*a(n-21) -214551956*a(n-22) +84757573*a(n-23) +13317994*a(n-24) -10733620*a(n-25) +1466700*a(n-26) -21780*a(n-27) -2160*a(n-28)

A221896 Number of nX4 arrays of occupancy after each element stays put or moves to some horizontal, vertical or antidiagonal neighbor, without move-in move-out straight through or left turns.

Original entry on oeis.org

13, 2241, 236532, 25821731, 2814706089, 307131177266, 33498766685333, 3653989849310339, 398568427571535443, 43474867097541833158, 4742132126980966864298, 517260183698295861792396

Offset: 1

R. H. Hardin Jan 30 2013

nonn

Column 4 of A221898

			Some solutions for n=3
..1..2..1..0....1..0..2..1....0..2..2..0....0..1..0..2....1..1..0..0
..0..1..1..2....0..3..1..1....1..0..0..1....2..3..0..1....0..2..4..1
..1..0..3..0....0..1..2..0....0..5..0..1....0..2..0..1....1..1..0..1

R. H. Hardin, Table of n, a(n) for n = 1..58

A221897 Number of nX5 arrays of occupancy after each element stays put or moves to some horizontal, vertical or antidiagonal neighbor, without move-in move-out straight through or left turns.

Original entry on oeis.org

28, 19408, 7235107, 2815434576, 1093046005330, 424750933848720, 164973176599593177, 64079516472337724523, 24889801648272710871176, 9667694294893797006224411, 3755123558818256978843191913

Offset: 1

R. H. Hardin Jan 30 2013

nonn

Column 5 of A221898

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

R. H. Hardin, Table of n, a(n) for n = 1..16

A221899 Number of 2 X n arrays of occupancy after each element stays put or moves to some horizontal, vertical or antidiagonal neighbor, without move-in move-out straight through or left turns.

Original entry on oeis.org

3, 31, 258, 2241, 19408, 167960, 1453952, 12585637, 108943526, 943035150, 8163084148, 70661144632, 611655753520, 5294603734144, 45831055372945, 396721972412987, 3434097733826959, 29726176177614458, 257315201439500033

Offset: 1

R. H. Hardin, Jan 30 2013

nonn

Row 2 of A221898.

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

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

Cf. A221898.

Empirical: a(n) = 5*a(n-1) + 26*a(n-2) + 45*a(n-3) + 34*a(n-4) - 2*a(n-5) - 4*a(n-6) + a(n-7).

Empirical g.f.: x*(3 + 16*x + 25*x^2 + 10*x^3 - 2*x^4 - 4*x^5 + x^6) / (1 - 5*x - 26*x^2 - 45*x^3 - 34*x^4 + 2*x^5 + 4*x^6 - x^7). - Colin Barker, Aug 11 2018

A221900 Number of 3Xn arrays of occupancy after each element stays put or moves to some horizontal, vertical or antidiagonal neighbor, without move-in move-out straight through or left turns.

Original entry on oeis.org

6, 266, 7667, 236532, 7235107, 221465158, 6778558415, 207481075456, 6350624324828, 194381582401875, 5949680932424079, 182109354161412326, 5574049625663873593, 170611934699230942606, 5222133675326885401935

Offset: 1

R. H. Hardin Jan 30 2013

nonn

Row 3 of A221898

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

R. H. Hardin, Table of n, a(n) for n = 1..129

Empirical: a(n) = 14*a(n-1) +401*a(n-2) +3090*a(n-3) +7741*a(n-4) -40484*a(n-5) -361940*a(n-6) -1090743*a(n-7) -1171988*a(n-8) +2002414*a(n-9) +720120*a(n-10) -7394610*a(n-11) +17527526*a(n-12) -2069693*a(n-13) -44623518*a(n-14) +78779650*a(n-15) -104778098*a(n-16) +119555094*a(n-17) +11992813*a(n-18) -174397406*a(n-19) +103166505*a(n-20) +131329969*a(n-21) -214551956*a(n-22) +84757573*a(n-23) +13317994*a(n-24) -10733620*a(n-25) +1466700*a(n-26) -21780*a(n-27) -2160*a(n-28)

A221901 Number of 4 X n arrays of occupancy after each element stays put or moves to some horizontal, vertical or antidiagonal neighbor, without move-in move-out straight through or left turns.

Original entry on oeis.org

13, 2305, 235332, 25821731, 2815434576, 307126807101, 33499434763000, 3654072363322660, 398576690257243663, 43475776796985596792, 4742231413650315959473

Offset: 1

R. H. Hardin Jan 30 2013

nonn

Row 4 of A221898.

			Some solutions for n=3
..1..0..1....0..2..0....0..1..2....0..2..1....0..0..2....0..0..0....0..2..1
..0..3..2....1..1..2....2..0..1....2..0..1....4..0..0....2..2..2....1..1..0
..1..0..1....0..0..3....1..0..2....0..2..4....1..0..0....1..0..0....2..2..2
..2..0..1....2..1..0....0..3..0....0..0..0....0..5..0....2..1..2....0..0..1

Cf. A221898.

cp's OEIS Frontend

A221894 Number of n X 2 arrays of occupancy after each element stays put or moves to some horizontal, vertical or antidiagonal neighbor, without move-in move-out straight through or left turns.

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A221895 Number of nX3 arrays of occupancy after each element stays put or moves to some horizontal, vertical or antidiagonal neighbor, without move-in move-out straight through or left turns.

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A221896 Number of nX4 arrays of occupancy after each element stays put or moves to some horizontal, vertical or antidiagonal neighbor, without move-in move-out straight through or left turns.

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A221897 Number of nX5 arrays of occupancy after each element stays put or moves to some horizontal, vertical or antidiagonal neighbor, without move-in move-out straight through or left turns.

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A221899 Number of 2 X n arrays of occupancy after each element stays put or moves to some horizontal, vertical or antidiagonal neighbor, without move-in move-out straight through or left turns.

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A221900 Number of 3Xn arrays of occupancy after each element stays put or moves to some horizontal, vertical or antidiagonal neighbor, without move-in move-out straight through or left turns.

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A221901 Number of 4 X n arrays of occupancy after each element stays put or moves to some horizontal, vertical or antidiagonal neighbor, without move-in move-out straight through or left turns.

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