A280859 -id:A280859 - cp's OEIS frontend

A280853 Number of n X 2 0..2 arrays with no element equal to more than one of its king-move neighbors and with new values introduced in order 0 sequentially upwards.

2, 9, 29, 110, 442, 1708, 6596, 25624, 99432, 385584, 1495696, 5802080, 22506144, 87301312, 338644032, 1313606016, 5095497344, 19765519104, 76670777600, 297407202816, 1153647430144, 4475017382912, 17358666073088, 67334551345152

Offset: 1

R. H. Hardin, Jan 09 2017

nonn

Column 2 of A280859.

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

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

Cf. A280859.

Empirical: a(n) = 4*a(n-1) - 2*a(n-2) + 8*a(n-3) - 8*a(n-4) for n>5.

Empirical g.f.: x*(1 - x)*(2 + 3*x - 4*x^3) / (1 - 4*x + 2*x^2 - 8*x^3 + 8*x^4). - Colin Barker, Mar 22 2018

A280854 Number of n X 3 0..2 arrays with no element equal to more than one of its king-move neighbors and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

4, 29, 46, 96, 256, 678, 1698, 4358, 11218, 28650, 73354, 188066, 481554, 1233194, 3159018, 8091050, 20722730, 53077762, 135947682, 348198514, 891836994, 2284251018, 5850611770, 14985083066, 38381073050, 98304843826, 251786685106

Offset: 1

R. H. Hardin, Jan 09 2017

nonn

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

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

Column 3 of A280859.

Empirical: a(n) = 2*a(n-1) + 4*a(n-3) - a(n-4) + 2*a(n-6) - 2*a(n-7) for n>9.

Empirical g.f.: x*(4 + 21*x - 12*x^2 - 12*x^3 - 48*x^4 + 11*x^5 - 4*x^6 - 16*x^7 + 12*x^8) / (1 - 2*x - 4*x^3 + x^4 - 2*x^6 + 2*x^7). - Colin Barker, Feb 14 2019

A280855 Number of nX4 0..2 arrays with no element equal to more than one of its king-move neighbors and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

11, 110, 96, 124, 216, 462, 1005, 2010, 3907, 7756, 15749, 31804, 63463, 126758, 254453, 511180, 1024877, 2052836, 4115191, 8254198, 16552251, 33182160, 66522097, 133381078, 267442273, 536212952, 1075064777, 2155474072, 4321733703

Offset: 1

R. H. Hardin, Jan 09 2017

nonn

Column 4 of A280859.

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

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

Cf. A280859.

Empirical: a(n) = a(n-1) +a(n-2) +a(n-3) +2*a(n-4) +3*a(n-5) -4*a(n-6) -3*a(n-7) -4*a(n-10) +2*a(n-12) for n>16

A280856 Number of nX5 0..2 arrays with no element equal to more than one of its king-move neighbors and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

30, 442, 256, 216, 282, 491, 968, 1857, 3220, 5281, 8574, 14339, 24694, 42833, 73650, 125361, 212438, 360727, 614668, 1049609, 1791800, 3055487, 5205640, 8868669, 15113516, 25765385, 43926544, 74885231, 127643494, 217567203, 370837946

Offset: 1

R. H. Hardin, Jan 09 2017

nonn

Column 5 of A280859.

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

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

Cf. A280859.

Empirical: a(n) = a(n-1) +a(n-2) -a(n-3) +2*a(n-4) -a(n-5) +4*a(n-6) -a(n-7) -a(n-8) -2*a(n-9) -3*a(n-12) for n>18

A280857 Number of nX6 0..2 arrays with no element equal to more than one of its king-move neighbors and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

82, 1708, 678, 462, 491, 712, 1202, 2268, 4220, 7108, 11240, 17330, 26934, 43062, 70776, 117452, 193842, 316394, 511776, 825074, 1333130, 2163076, 3521462, 5738446, 9343090, 15187700, 24659768, 40027188, 64994524, 105599072, 171639520

Offset: 1

R. H. Hardin, Jan 09 2017

nonn

Column 6 of A280859.

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

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

Cf. A280859.

Empirical: a(n) = a(n-1) +a(n-2) -a(n-3) +a(n-4) +6*a(n-7) -5*a(n-8) +3*a(n-9) -3*a(n-10) -3*a(n-11) +2*a(n-12) -4*a(n-13) +a(n-14) -2*a(n-15) -2*a(n-16) for n>22

A280858 Number of nX7 0..2 arrays with no element equal to more than one of its king-move neighbors and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

224, 6596, 1698, 1005, 968, 1202, 1738, 2877, 5244, 9569, 15872, 24653, 36954, 55077, 83190, 128817, 204084, 326793, 522262, 828099, 1300592, 2029441, 3159306, 4927841, 7712840, 12114811, 19061740, 29999825, 47157384, 74031085, 116080358

Offset: 1

R. H. Hardin, Jan 09 2017

nonn

Column 7 of A280859.

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

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

Cf. A280859.

Empirical: a(n) = a(n-1) +a(n-2) -a(n-3) +a(n-4) -a(n-5) +2*a(n-6) -a(n-7) +6*a(n-8) -4*a(n-9) -4*a(n-12) -a(n-13) -2*a(n-14) -3*a(n-15) -3*a(n-16) +3*a(n-17) -3*a(n-18) +a(n-19) -a(n-20) +2*a(n-23) for n>29

A280852 Number of n X n 0..2 arrays with no element equal to more than one of its king-move neighbors and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

1, 9, 46, 124, 282, 712, 1738, 4124, 9562, 21752, 48730, 107992, 237082, 516376, 1117210

Offset: 1

R. H. Hardin, Jan 09 2017

nonn

Diagonal of A280859.

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

Cf. A280859.

cp's OEIS Frontend

A280853 Number of n X 2 0..2 arrays with no element equal to more than one of its king-move neighbors and with new values introduced in order 0 sequentially upwards.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A280854 Number of n X 3 0..2 arrays with no element equal to more than one of its king-move neighbors and with new values introduced in order 0 sequentially upwards.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A280855 Number of nX4 0..2 arrays with no element equal to more than one of its king-move neighbors and with new values introduced in order 0 sequentially upwards.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A280856 Number of nX5 0..2 arrays with no element equal to more than one of its king-move neighbors and with new values introduced in order 0 sequentially upwards.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A280857 Number of nX6 0..2 arrays with no element equal to more than one of its king-move neighbors and with new values introduced in order 0 sequentially upwards.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A280858 Number of nX7 0..2 arrays with no element equal to more than one of its king-move neighbors and with new values introduced in order 0 sequentially upwards.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A280852 Number of n X n 0..2 arrays with no element equal to more than one of its king-move neighbors and with new values introduced in order 0 sequentially upwards.

Views

Author

Keywords

Comments

Examples

Crossrefs