A198906 -id:A198906 - cp's OEIS frontend

A198899 Number of n X n 0..4 arrays with values 0..4 introduced in row major order and no element equal to any horizontal or vertical neighbor.

1, 4, 1211, 6907736, 423503301834, 274342896958292170, 1877611081501313948217870, 135766460737448561825230968357842

Offset: 1

R. H. Hardin Oct 31 2011

nonn

Diagonal of A198906

			Some solutions with values 0 to 4 for n=4
..0..1..0..1....0..1..0..1....0..1..0..1....0..1..0..1....0..1..0..1
..1..2..1..0....1..2..1..2....1..2..1..2....1..0..2..0....1..0..1..0
..0..1..3..4....2..3..0..1....3..0..2..0....3..4..0..3....2..1..0..3
..3..2..0..3....4..1..2..4....4..3..1..3....2..1..2..4....1..4..1..2

Jean-François Alcover, Table of n, a(n) for n = 1..14

A198906 = Cases[Import["https://oeis.org/A198906/b198906.txt", "Table"], {, }][[All, 2]];
a[n_] := A198906[[2 n^2 - 2 n + 1]];
Table[a[n], {n, 1, 14}] (* Jean-François Alcover, Sep 23 2019 *)

A198901 Number of n X 3 0..4 arrays with values 0..4 introduced in row major order and no element equal to any horizontal or vertical neighbor.

Original entry on oeis.org

2, 33, 1211, 50384, 2125425, 89793204, 3794115705, 160319061892, 6774239755817, 286243775060868, 12095158053422201, 511077834439270724, 21595464215307153225, 912510860892666556164, 38557914891188891686425

Offset: 1

R. H. Hardin, Oct 31 2011

nonn

Column 3 of A198906.

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

R. H. Hardin, Table of n, a(n) for n = 1..200

Cf. A198906.

Empirical: a(n) = 51*a(n-1) - 393*a(n-2) + 1013*a(n-3) - 902*a(n-4) + 232*a(n-5).

Empirical g.f.: x*(2 - 69*x + 314*x^2 - 434*x^3 + 139*x^4) / ((1 - x)*(1 - 5*x + 2*x^2)*(1 - 45*x + 116*x^2)). - Colin Barker, Mar 02 2018

A198902 Number of nX4 0..4 arrays with values 0..4 introduced in row major order and no element equal to any horizontal or vertical neighbor.

Original entry on oeis.org

5, 380, 50384, 6907736, 948656912, 130292546801, 17895005957823, 2457786852894234, 337564362706067534, 46362726246946052884, 6367681611531782236418, 874568266109492180669275

Offset: 1

R. H. Hardin Oct 31 2011

nonn

Column 4 of A198906

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

R. H. Hardin, Table of n, a(n) for n = 1..200

Empirical: a(n) = 163*a(n-1) -3751*a(n-2) +32097*a(n-3) -120287*a(n-4) +201471*a(n-5) -148296*a(n-6) +38604*a(n-7)

A198903 Number of n X 5 0..4 arrays with values 0..4 introduced in row major order and no element equal to any horizontal or vertical neighbor.

Original entry on oeis.org

15, 4801, 2125425, 948656912, 423503301834, 189062985604305, 84402688527136201, 37679579867128064832, 16821155393975907014458, 7509406150309683843851949, 3352396396661126098060061297

Offset: 1

R. H. Hardin Oct 31 2011

nonn

Column 5 of A198906.

			Some solutions with values 0 to 4 for n=4
..0..1..0..2..1....0..1..0..1..2....0..1..0..2..3....0..1..0..2..3
..1..0..2..0..2....1..0..3..4..0....1..0..2..3..4....1..0..2..1..4
..0..1..0..1..3....0..1..2..1..2....0..1..3..0..1....0..1..0..3..0
..1..0..4..2..1....1..0..3..2..3....1..0..2..1..4....1..0..3..1..4

R. H. Hardin, Table of n, a(n) for n = 1..200

Cf. A198906.

Empirical: a(n) = 559*a(n-1) -54943*a(n-2) +2182857*a(n-3) -41132051*a(n-4) +348302393*a(n-5) -519526889*a(n-6) -11351340633*a(n-7) +79466721924*a(n-8) -227367989480*a(n-9) +329414183656*a(n-10) -247117199296*a(n-11) +89130224384*a(n-12) -11964372480*a(n-13).

A198904 Number of nX6 0..4 arrays with values 0..4 introduced in row major order and no element equal to any horizontal or vertical neighbor.

Original entry on oeis.org

51, 62004, 89793204, 130292546801, 189062985604305, 274342896958292170, 398089706066811447174, 577654521153750977585383, 838214957290859115489996817, 1216305402162613228248847610489

Offset: 1

R. H. Hardin Oct 31 2011

nonn

Column 6 of A198906

			Some solutions with values 0 to 4 for n=4
..0..1..0..2..3..4....0..1..0..2..0..3....0..1..0..2..3..0....0..1..0..2..0..3
..1..0..1..0..2..1....1..0..1..0..3..2....1..0..1..0..4..3....1..0..1..0..3..0
..0..1..0..2..1..4....0..1..0..3..4..0....0..1..0..2..3..1....0..1..0..3..0..1
..1..0..1..4..2..0....1..0..1..2..1..4....1..0..1..0..2..0....1..0..1..4..1..4

R. H. Hardin, Table of n, a(n) for n = 1..100

Empirical: a(n) = 1941*a(n-1) -806387*a(n-2) +148087843*a(n-3) -14409929271*a(n-4) +778094676063*a(n-5) -21816737058431*a(n-6) +172301552678113*a(n-7) +7343185920165785*a(n-8) -245567930834154099*a(n-9) +3173967512676632848*a(n-10) -15227320856420081570*a(n-11) -91185217544269175883*a(n-12) +1851754850894045611993*a(n-13) -13021262413927953929580*a(n-14) +53026970301996239080604*a(n-15) -137791962761820102384680*a(n-16) +234523646685947458039624*a(n-17) -259529910793881853229984*a(n-18) +179240545997964052307808*a(n-19) -69895831119161489802880*a(n-20) +11699525896373883270144*a(n-21)

A198905 Number of nX7 0..4 arrays with values 0..4 introduced in row major order and no element equal to any horizontal or vertical neighbor.

Original entry on oeis.org

187, 804833, 3794115705, 17895005957823, 84402688527136201, 398089706066811447174, 1877611081501313948217870, 8855851690895754550489882369, 41769091588504560613470987916898

Offset: 1

R. H. Hardin Oct 31 2011

nonn

Column 7 of A198906

			Some solutions with values 0 to 4 for n=4
..0..1..0..1..0..2..3....0..1..0..1..0..2..0....0..1..0..1..0..2..1
..1..0..1..0..1..3..2....1..0..1..0..3..0..2....1..0..1..0..3..4..3
..0..1..0..2..0..2..3....0..1..0..2..4..2..4....0..1..0..2..0..1..0
..1..0..2..0..2..4..1....1..0..2..0..2..1..3....1..0..2..0..2..0..2

R. H. Hardin, Table of n, a(n) for n = 1..27

cp's OEIS Frontend

A198899 Number of n X n 0..4 arrays with values 0..4 introduced in row major order and no element equal to any horizontal or vertical neighbor.

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A198901 Number of n X 3 0..4 arrays with values 0..4 introduced in row major order and no element equal to any horizontal or vertical neighbor.

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A198902 Number of nX4 0..4 arrays with values 0..4 introduced in row major order and no element equal to any horizontal or vertical neighbor.

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A198903 Number of n X 5 0..4 arrays with values 0..4 introduced in row major order and no element equal to any horizontal or vertical neighbor.

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A198904 Number of nX6 0..4 arrays with values 0..4 introduced in row major order and no element equal to any horizontal or vertical neighbor.

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A198905 Number of nX7 0..4 arrays with values 0..4 introduced in row major order and no element equal to any horizontal or vertical neighbor.

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