A241108 -id:A241108 - cp's OEIS frontend

A241103 Number of n X 3 0..2 arrays with no element equal to one or three horizontal or vertical neighbors, with new values 0..2 introduced in row major order.

2, 11, 58, 294, 1522, 7846, 40418, 208374, 1074002, 5535686, 28533058, 147068694, 758041522, 3907203046, 20139040418, 103803409974, 535037802002, 2757765332486, 14214452973058, 73266086411094, 377638128337522

Offset: 1

R. H. Hardin, Apr 16 2014

nonn

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

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

Column 3 of A241108.

Empirical: a(n) = 3*a(n-1) + 8*a(n-2) + 16*a(n-3).

Empirical g.f.: x*(2 + 5*x + 9*x^2) / (1 - 3*x - 8*x^2 - 16*x^3). - Colin Barker, Oct 29 2018

A241104 Number of nX4 0..2 arrays with no element equal to one or three horizontal or vertical neighbors, with new values 0..2 introduced in row major order.

Original entry on oeis.org

4, 36, 294, 2436, 19814, 162776, 1333934, 10937316, 89651534, 734979136, 6025149574, 49393306556, 404916355574, 3319433387656, 27212098788254, 223079838087956, 1828767624421854, 14991902921730896, 122900877847563254

Offset: 1

R. H. Hardin, Apr 16 2014

nonn

Column 4 of A241108

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

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

Empirical: a(n) = 6*a(n-1) +21*a(n-2) -12*a(n-3) +8*a(n-4) -688*a(n-5) -1648*a(n-6) -768*a(n-7) -2304*a(n-8) +8192*a(n-9) +16384*a(n-10)

A241105 Number of nX5 0..2 arrays with no element equal to one or three horizontal or vertical neighbors, with new values 0..2 introduced in row major order.

Original entry on oeis.org

8, 116, 1522, 19814, 259388, 3374086, 44030862, 574246744, 7489718098, 97685897406, 1274061880332, 16617079770494, 216729255718838, 2826706576812536, 36867513064014682, 480847045785788134

Offset: 1

R. H. Hardin, Apr 16 2014

nonn

Column 5 of A241108

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

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

Empirical: a(n) = 14*a(n-1) +2*a(n-2) -175*a(n-3) -54*a(n-4) +1648*a(n-5) -42588*a(n-6) -24344*a(n-7) +167248*a(n-8) +247904*a(n-9) -88832*a(n-10) +33429248*a(n-11) +48635904*a(n-12) +27281408*a(n-13) -32276480*a(n-14) -600080384*a(n-15) -9134145536*a(n-16) -11089739776*a(n-17) -2071986176*a(n-18) +11282677760*a(n-19) +94019518464*a(n-20) +716320014336*a(n-21) +518617300992*a(n-22) +438086664192*a(n-23) +618475290624*a(n-24) -6597069766656*a(n-25) -17592186044416*a(n-26)

A241106 Number of nX6 0..2 arrays with no element equal to one or three horizontal or vertical neighbors, with new values 0..2 introduced in row major order.

Original entry on oeis.org

16, 376, 7846, 162776, 3374086, 70145916, 1454236806, 30189380016, 626548445696, 13004327687556, 269904513767276, 5601924832399656, 116268494681555446, 2413172096267222836, 50085748850277170776, 1039537719846439186376

Offset: 1

R. H. Hardin, Apr 16 2014

nonn

Column 6 of A241108

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 76

Empirical recurrence of order 76 (see link above)

A241107 Number of nX7 0..2 arrays with no element equal to one or three horizontal or vertical neighbors, with new values 0..2 introduced in row major order.

Original entry on oeis.org

32, 1216, 40418, 1333934, 44030862, 1454236806, 48054344508, 1586763763374, 52415988665902, 1731396543937826, 57192293520907518, 1889201414043365704, 62405079297467322902, 2061398474689109752446, 68093252520609897541958

Offset: 1

R. H. Hardin, Apr 16 2014

nonn

Column 7 of A241108

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

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

cp's OEIS Frontend

A241103 Number of n X 3 0..2 arrays with no element equal to one or three horizontal or vertical neighbors, with new values 0..2 introduced in row major order.

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A241104 Number of nX4 0..2 arrays with no element equal to one or three horizontal or vertical neighbors, with new values 0..2 introduced in row major order.

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A241105 Number of nX5 0..2 arrays with no element equal to one or three horizontal or vertical neighbors, with new values 0..2 introduced in row major order.

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A241106 Number of nX6 0..2 arrays with no element equal to one or three horizontal or vertical neighbors, with new values 0..2 introduced in row major order.

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A241107 Number of nX7 0..2 arrays with no element equal to one or three horizontal or vertical neighbors, with new values 0..2 introduced in row major order.

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