A222020 -id:A222020 - cp's OEIS frontend

A222017 Number of nX4 arrays of occupancy after each element stays put or moves to some horizontal or vertical neighbor, without move-in move-out straight through or left turns.

13, 1363, 86088, 5925053, 403317044, 27460842224, 1870475750419, 127385479747138, 8675741759311142, 590866503322144180, 40241368935424750183, 2740665723881270704902, 186654894043998446085330

Offset: 1

R. H. Hardin Feb 05 2013

nonn

Column 4 of A222020

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

R. H. Hardin, Table of n, a(n) for n = 1..131

A222015 Number of n X 2 arrays of occupancy after each element stays put or moves to some horizontal or vertical neighbor, without move-in move-out straight through or left turns.

Original entry on oeis.org

3, 27, 188, 1363, 9838, 70994, 512456, 3698699, 26696370, 192687348, 1390767557, 10038200482, 72453134112, 522947981192, 3774503253017, 27243388115499, 196635728242591, 1419265821803368, 10243893573843252, 73937773981558032

Offset: 1

R. H. Hardin, Feb 05 2013

nonn

Column 2 of A222020.

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

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

Cf. A222020.

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 + x)*(3 + 15*x + 17*x^2 - 13*x^3 - 21*x^4 + 5*x^5 + 5*x^6 - x^7) / (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 14 2018

A222016 Number of nX3 arrays of occupancy after each element stays put or moves to some horizontal or vertical neighbor, without move-in move-out straight through or left turns.

Original entry on oeis.org

6, 188, 3875, 86088, 1892859, 41636522, 916164266, 20156123913, 443464985963, 9756801621038, 214662580479904, 4722860659023550, 103909179716386461, 2286139384890550049, 50298089904801491960, 1106624498857041822230

Offset: 1

R. H. Hardin Feb 05 2013

nonn

Column 3 of A222020

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

R. H. Hardin, Table of n, a(n) for n = 1..195

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)

A222018 Number of nX5 arrays of occupancy after each element stays put or moves to some horizontal or vertical neighbor, without move-in move-out straight through or left turns.

Original entry on oeis.org

28, 9838, 1892859, 403317044, 84799061141, 17838051289367, 3753835631741568, 789821887272883642, 166189333434443018741, 34968169848205865653334, 7357721396433443050132543, 1548152408282663670986074421

Offset: 1

R. H. Hardin Feb 05 2013

nonn

Column 5 of A222020

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

R. H. Hardin, Table of n, a(n) for n = 1..29

A222019 Number of nX6 arrays of occupancy after each element stays put or moves to some horizontal or vertical neighbor, without move-in move-out straight through or left turns.

Original entry on oeis.org

60, 70994, 41636522, 27460842224, 17838051289367, 11593944359617570, 7538777970648890706, 4901063986390211477492, 3186408336556340539334545

Offset: 1

R. H. Hardin Feb 05 2013

nonn

Column 6 of A222020

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

cp's OEIS Frontend

A222017 Number of nX4 arrays of occupancy after each element stays put or moves to some horizontal or vertical neighbor, without move-in move-out straight through or left turns.

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A222015 Number of n X 2 arrays of occupancy after each element stays put or moves to some horizontal or vertical neighbor, without move-in move-out straight through or left turns.

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A222016 Number of nX3 arrays of occupancy after each element stays put or moves to some horizontal or vertical neighbor, without move-in move-out straight through or left turns.

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A222018 Number of nX5 arrays of occupancy after each element stays put or moves to some horizontal or vertical neighbor, without move-in move-out straight through or left turns.

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A222019 Number of nX6 arrays of occupancy after each element stays put or moves to some horizontal or vertical neighbor, without move-in move-out straight through or left turns.

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