A221937 -id:A221937 - cp's OEIS frontend

A221933 Number of n X 3 arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without move-in move-out straight through or left turns.

6, 105, 1599, 24535, 376389, 5773962, 88575493, 1358791848, 20844539836, 319765562424, 4905362062396, 75250682972713, 1154382737872290, 17708802802243865, 271661803663808763, 4167426584055854255

Offset: 1

R. H. Hardin, Feb 01 2013

nonn

Column 3 of A221937.

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

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

Cf. A221937.

Empirical: a(n) = 14*a(n-1) + 21*a(n-2) - 5*a(n-3) - 26*a(n-4) + a(n-5).

Empirical g.f.: x*(6 + 21*x + 3*x^2 - 26*x^3 + x^4) / (1 - 14*x - 21*x^2 + 5*x^3 + 26*x^4 - x^5). - Colin Barker, Aug 11 2018

A221934 Number of n X 4 arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without move-in move-out straight through or left turns.

Original entry on oeis.org

13, 783, 36467, 1759041, 84547866, 4065176472, 195452177326, 9397301189681, 451820171352622, 21723415149940892, 1044457051240660759, 50217266705524767168, 2414435205611270005630, 116085516886164224493024

Offset: 1

R. H. Hardin, Feb 01 2013

nonn

Column 4 of A221937.

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

R. H. Hardin, Table of n, a(n) for n = 1..157

Cf. A221937.

Empirical: a(n) = 45*a(n-1) +166*a(n-2) -812*a(n-3) -2452*a(n-4) +2243*a(n-5) +23138*a(n-6) +2192*a(n-7) +908*a(n-8) +6885*a(n-9) -5028*a(n-10) +3940*a(n-11) -628*a(n-12) +36*a(n-13).

A221935 Number of nX5 arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without move-in move-out straight through or left turns.

Original entry on oeis.org

28, 5622, 799632, 119035112, 17626884659, 2611330803361, 386840503637732, 57306383975427486, 8489341273827367120, 1257607107085271304144, 186301337661284652338010, 27598594360590020663604925

Offset: 1

R. H. Hardin Feb 01 2013

nonn

Column 5 of A221937

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

R. H. Hardin, Table of n, a(n) for n = 1..125

Empirical: a(n) = 139*a(n-1) +1565*a(n-2) -28842*a(n-3) -369727*a(n-4) +1342456*a(n-5) +27113117*a(n-6) +34514978*a(n-7) -1040783248*a(n-8) -752172735*a(n-9) -7514497431*a(n-10) +3813284858*a(n-11) -7857119331*a(n-12) +165551321671*a(n-13) +153295270688*a(n-14) +67167089407*a(n-15) +194143861216*a(n-16) -17802740958*a(n-17) +352253527909*a(n-18) -217093267050*a(n-19) -103711174603*a(n-20) +24768760853*a(n-21) +6245517002*a(n-22) +10757772379*a(n-23) -253702884*a(n-24) -2234119424*a(n-25) +988262416*a(n-26) +31172608*a(n-27) -79610304*a(n-28) +7948800*a(n-29)

A221936 Number of nX6 arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without move-in move-out straight through or left turns.

Original entry on oeis.org

60, 40608, 17595404, 8118923949, 3719159201319, 1705064784016177, 781631768770230485, 358315975721236723937, 164259260168423743838749, 75299755989611523426077650, 34518925873564465982979613568

Offset: 1

R. H. Hardin Feb 01 2013

nonn

Column 6 of A221937

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

R. H. Hardin, Table of n, a(n) for n = 1..31

A221938 Number of 2 X n arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without move-in move-out straight through or left turns.

Original entry on oeis.org

1, 17, 105, 783, 5622, 40608, 293084, 2115379, 15268366, 110202874, 795416273, 5741108247, 41437835079, 299087573904, 2158736742330, 15581203397143, 112461095655909, 811715097631008, 5858749604657939, 42286939137094085

Offset: 1

R. H. Hardin, Feb 01 2013

nonn

Row 2 of A221937.

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

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

Cf. A221937.

Empirical: a(n) = 3*a(n-1) + 25*a(n-2) + 40*a(n-3) + a(n-4) - 42*a(n-5) - 20*a(n-6) + 10*a(n-7) + 4*a(n-8) -a(n-9).

Empirical g.f.: x*(1 + 14*x + 29*x^2 + 3*x^3 - 33*x^4 - 8*x^5 + 19*x^6 + 4*x^7 - x^8) / (1 - 3*x - 25*x^2 - 40*x^3 - x^4 + 42*x^5 + 20*x^6 - 10*x^7 - 4*x^8 + x^9). - Colin Barker, Aug 11 2018

A221939 Number of 3Xn arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without move-in move-out straight through or left turns.

Original entry on oeis.org

1, 91, 1599, 36467, 799632, 17595404, 387146025, 8517616158, 187399250327, 4123030670649, 90712135220235, 1995786856338823, 43909951229853113, 966076992787974879, 21254971544597958477, 467637484141672483673

Offset: 1

R. H. Hardin Feb 01 2013

nonn

Row 3 of A221937

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

R. H. Hardin, Table of n, a(n) for n = 1..98

Empirical: a(n) = 6*a(n-1) +286*a(n-2) +1731*a(n-3) -3366*a(n-4) -58755*a(n-5) -73158*a(n-6) +744580*a(n-7) +1606773*a(n-8) -5847271*a(n-9) -13299665*a(n-10) +35585397*a(n-11) +56858689*a(n-12) -168213873*a(n-13) -99886051*a(n-14) +532060381*a(n-15) -127805646*a(n-16) -951724652*a(n-17) +874261131*a(n-18) +729065885*a(n-19) -1511277493*a(n-20) +275583551*a(n-21) +992093720*a(n-22) -708567632*a(n-23) -119679569*a(n-24) +310913349*a(n-25) -92576435*a(n-26) -25624476*a(n-27) +17876348*a(n-28) -1254086*a(n-29) -1085212*a(n-30) +391330*a(n-31) -46391*a(n-32) -25190*a(n-33) +7306*a(n-34) +873*a(n-35) -236*a(n-36) -12*a(n-37) for n>38

A221940 Number of 4Xn arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without move-in move-out straight through or left turns.

Original entry on oeis.org

1, 489, 24535, 1759041, 119035112, 8118923949, 552777330287, 37650441405451, 2564181255574899, 174635497977344862, 11893675692936218866, 810026663520753630706, 55167419097633745309553, 3757214394165203187203557

Offset: 1

R. H. Hardin Feb 01 2013

nonn

Row 4 of A221937

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

R. H. Hardin, Table of n, a(n) for n = 1..24

A221941 Number of 5Xn arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without move-in move-out straight through or left turns.

Original entry on oeis.org

1, 2627, 376389, 84547866, 17626884659, 3719159201319, 782051177169672, 164583386567947853, 34629683921533060992, 7286522628060662000197

Offset: 1

R. H. Hardin Feb 01 2013

nonn

Row 5 of A221937

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

cp's OEIS Frontend

A221933 Number of n X 3 arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without move-in move-out straight through or left turns.

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A221934 Number of n X 4 arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without move-in move-out straight through or left turns.

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A221935 Number of nX5 arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without move-in move-out straight through or left turns.

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A221936 Number of nX6 arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without move-in move-out straight through or left turns.

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A221938 Number of 2 X n arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without move-in move-out straight through or left turns.

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A221939 Number of 3Xn arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without move-in move-out straight through or left turns.

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A221940 Number of 4Xn arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without move-in move-out straight through or left turns.

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A221941 Number of 5Xn arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without move-in move-out straight through or left turns.

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