A280673 -id:A280673 - cp's OEIS frontend

A280668 Number of n X 3 0..2 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

4, 59, 858, 12484, 181640, 2642832, 38452768, 559481408, 8140361856, 118440917248, 1723295736320, 25073667646464, 364817712941056, 5308037322346496, 77231064216379392, 1123699197608083456

Offset: 1

R. H. Hardin, Jan 07 2017

nonn

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

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

Column 3 of A280673.

Empirical: a(n) = 14*a(n-1) + 8*a(n-2).
Conjectures from Colin Barker, Feb 14 2019: (Start)
G.f.: x*(4 + 3*x) / (1 - 14*x - 8*x^2).
a(n) = ((7-sqrt(57))^n*(-11+3*sqrt(57)) + (7+sqrt(57))^n*(11+3*sqrt(57))) / (16*sqrt(57)).
(End)

A280669 Number of n X 4 0..2 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

11, 338, 10205, 310365, 9439606, 287101721, 8732086113, 265582964074, 8077601392565, 245677069239189, 7472171430204190, 227263155064756577, 6912119473224669225, 210229395075140809474, 6394044362928373953677

Offset: 1

R. H. Hardin, Jan 07 2017

nonn

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

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

Column 4 of A280673.

Empirical: a(n) = 29*a(n-1) + 44*a(n-2) - 27*a(n-3) - 81*a(n-4) for n>5.

Empirical g.f.: x*(11 + 19*x - 81*x^2 - 155*x^3 + 18*x^4) / (1 - 29*x - 44*x^2 + 27*x^3 + 81*x^4). - Colin Barker, Feb 14 2019

A280670 Number of nX5 0..2 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

30, 1917, 119440, 7533245, 474736149, 29920114246, 1885698283255, 118845116023725, 7490149091439288, 472062591963218273, 29751489321018113345, 1875071509361980884750, 118175366862571989996619

Offset: 1

R. H. Hardin, Jan 07 2017

nonn

Column 5 of A280673.

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

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

Cf. A280673.

Empirical: a(n) = 59*a(n-1) +268*a(n-2) -869*a(n-3) -2331*a(n-4) +3754*a(n-5) -8240*a(n-6) -88*a(n-7) -3472*a(n-8) for n>9

A280671 Number of nX6 0..2 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

82, 10893, 1401470, 183331502, 23952262535, 3130289979912, 409089889172506, 53463025958093933, 6986960714513387194, 913109939977637081743, 119332252787740585439815, 15595259598595853987150831

Offset: 1

R. H. Hardin, Jan 07 2017

nonn

Column 6 of A280673.

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

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

Cf. A280673.

Empirical: a(n) = 115*a(n-1) +2093*a(n-2) -4155*a(n-3) -183686*a(n-4) -585648*a(n-5) +633260*a(n-6) +10692868*a(n-7) -4449787*a(n-8) -90326895*a(n-9) -58218792*a(n-10) -85358831*a(n-11) -153604102*a(n-12) +506925527*a(n-13) +114376456*a(n-14) +783370521*a(n-15) +27819835*a(n-16) +40476932*a(n-17) -4134454*a(n-18) +1119384*a(n-19) -261121*a(n-20) for n>22

A280672 Number of nX7 0..2 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

224, 61880, 16438612, 4460317695, 1208240638772, 327452072560351, 88741877287328326, 24049810737844448684, 6517703746847251930646, 1766353341829714295007100, 478696830022637290656991583

Offset: 1

R. H. Hardin, Jan 07 2017

nonn

Column 7 of A280673.

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

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

Cf. A280673.

A280674 Number of 2 X n 0..2 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

2, 11, 59, 338, 1917, 10893, 61880, 351541, 1997095, 11345458, 64453321, 366158041, 2080136592, 11817214849, 67133363931, 381383313234, 2166631062437, 12308588230773, 69924846394792, 397241669934877, 2256722073320511

Offset: 1

R. H. Hardin, Jan 07 2017

nonn

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

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

Row 2 of A280673.

Empirical: a(n) = 5*a(n-1) + 6*a(n-2) - 11*a(n-3) - 7*a(n-4) + 4*a(n-5) for n>6.

Empirical g.f.: x*(1 - x)*(2 + 3*x - x^2)*(1 - 2*x^2) / ((1 + x)*(1 - 6*x + 11*x^3 - 4*x^4)). - Colin Barker, Feb 14 2019

A280675 Number of 3Xn 0..2 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

5, 82, 858, 10205, 119440, 1401470, 16438612, 192831783, 2261964301, 26533504354, 311245493388, 3650998431229, 42827250423319, 502375841919309, 5893011645334528, 69126704336253119, 810875921978239834

Offset: 1

R. H. Hardin, Jan 07 2017

nonn

Row 3 of A280673.

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

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

Cf. A280673.

Empirical: a(n) = 11*a(n-1) +23*a(n-2) -160*a(n-3) -172*a(n-4) +690*a(n-5) +601*a(n-6) -513*a(n-7) -1314*a(n-8) -1903*a(n-9) +1720*a(n-10) +2445*a(n-11) -549*a(n-12) -998*a(n-13) +40*a(n-14) +136*a(n-15) +96*a(n-16) -32*a(n-17) -64*a(n-18) for n>20

A280676 Number of 4Xn 0..2 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

14, 612, 12484, 310365, 7533245, 183331502, 4460317695, 108520231044, 2640298250694, 64238619127022, 1562929767205929, 38026186043293995, 925179685380850290, 22509684536321285656, 547662154172647585113

Offset: 1

R. H. Hardin, Jan 07 2017

nonn

Row 4 of A280673.

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 73

Cf. A280673.

Empirical recurrence of order 73 (see link above)

A280677 Number of 5Xn 0..2 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

41, 4568, 181640, 9439606, 474736149, 23952262535, 1208240638772, 60949510593245, 3074564570571027, 155095359625755139, 7823728447342567501, 394665220545896300250, 19908746786901511218365, 1004289676988490253656371

Offset: 1

R. H. Hardin, Jan 07 2017

nonn

Row 5 of A280673.

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

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

Cf. A280673.

A280678 Number of 6Xn 0..2 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

122, 34096, 2642832, 287101721, 29920114246, 3130289979912, 327452072560351, 34253681605884733, 3583141682779617309, 374819732160862162533, 39208546724956189523288, 4101465758881532501508232

Offset: 1

R. H. Hardin, Jan 07 2017

nonn

Row 6 of A280673.

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

R. H. Hardin, Table of n, a(n) for n = 1..133

Cf. A280673.

cp's OEIS Frontend

A280668 Number of n X 3 0..2 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

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A280669 Number of n X 4 0..2 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

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A280670 Number of nX5 0..2 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

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A280671 Number of nX6 0..2 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

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A280672 Number of nX7 0..2 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

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A280674 Number of 2 X n 0..2 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

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A280675 Number of 3Xn 0..2 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

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A280676 Number of 4Xn 0..2 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

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A280677 Number of 5Xn 0..2 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

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Author

Keywords

Comments

Examples

Links

Crossrefs

A280678 Number of 6Xn 0..2 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

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