A269201 -id:A269201 - cp's OEIS frontend

A269196 Number of n X 3 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three no more than once.

60, 1284, 25572, 471492, 8314020, 142233732, 2380537188, 39186271044, 636703584804, 10237337586180, 163189207436004, 2582623154662596, 40622651914004388, 635603382950474628, 9899530341266770020

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

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

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

Column 3 of A269201.

Empirical: a(n) = 30*a(n-1) -237*a(n-2) +180*a(n-3) -36*a(n-4) for n>5.

Empirical g.f.: 12*x*(1 - 6*x)*(5 - 13*x + 28*x^2 - 12*x^3) / (1 - 15*x + 6*x^2)^2. - Colin Barker, Jan 20 2019

A269197 Number of n X 4 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three no more than once.

Original entry on oeis.org

216, 9612, 400428, 15289548, 555862380, 19558138380, 672230393004, 22702294138188, 756261535626732, 24917784636315276, 813662963240248620, 26370904678702613964, 849277413026034547308, 27202597468298860880652

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

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

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

Column 4 of A269201.

Empirical: a(n) = 62*a(n-1) - 1031*a(n-2) + 2180*a(n-3) - 1535*a(n-4) + 350*a(n-5) - 25*a(n-6) for n>7.

Empirical g.f.: 12*x*(18 - 315*x + 2265*x^2 - 8158*x^3 + 10756*x^4 - 4951*x^5 + 897*x^6) / ((1 - x)^2*(1 - 30*x + 5*x^2)^2). - Colin Barker, Jan 20 2019

A269198 Number of n X 5 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three no more than once.

Original entry on oeis.org

756, 68052, 5877228, 463790340, 34838403756, 2532677348772, 179867149105740, 12551707872624132, 864008559706781292, 58827234014669683044, 3969574872302454754188, 265864675607662372035012

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Column 5 of A269201.

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

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

Cf. A269201.

Empirical: a(n) = 156*a(n-1) -8170*a(n-2) +166732*a(n-3) -1381249*a(n-4) +2520764*a(n-5) +23584856*a(n-6) -130579860*a(n-7) +143100280*a(n-8) +633365472*a(n-9) -2425054036*a(n-10) +3486590032*a(n-11) -2082954096*a(n-12) -207585696*a(n-13) +891171072*a(n-14) -335167488*a(n-15) -34112320*a(n-16) +43766784*a(n-17) -8385024*a(n-18) +497664*a(n-19) -9216*a(n-20) for n>21.

A269199 Number of nX6 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three no more than once.

Original entry on oeis.org

2592, 472044, 84310620, 13753913556, 2135938293684, 320994710282892, 47121391706947500, 6796525936086462132, 966936595386067680804, 136062368474581143710892, 18974537404982889834704892

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Column 6 of A269201.

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 42

Cf. A269201.

Empirical recurrence of order 42 (see link above)

A269200 Number of n X 7 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three no more than once.

Original entry on oeis.org

8748, 3212820, 1184381844, 399104835612, 128136007344516, 39825831571425924, 12093315071771856492, 3608384928930423012804, 1062048602869077147571956, 309185374985245150329134076, 89206481105125372533736647588

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Column 7 of A269201.

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

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

Cf. A269201.

A269202 Number of 2 X n 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three no more than once.

Original entry on oeis.org

16, 180, 1284, 9612, 68052, 472044, 3212820, 21562476, 143085588, 940780908, 6138286356, 39791327340, 256517615124, 1645723601772, 10514049071892, 66922539204204, 424564703856660, 2685565034934636, 16942451080369428

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

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

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

Row 2 of A269201.

Empirical: a(n) = 10*a(n-1) - 13*a(n-2) - 60*a(n-3) - 36*a(n-4).
Conjectures from Colin Barker, Jan 20 2019: (Start)
G.f.: 4*x*(4 + 5*x - 77*x^2 + 18*x^3) / ((1 + x)^2*(1 - 6*x)^2).
a(n) = (6*(-678*(-1)^n+335*6^n) + 56*(144*(-1)^n+25*6^n)*n) / 1029.
(End)

A269203 Number of 3 X n 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three no more than once.

Original entry on oeis.org

64, 1740, 25572, 400428, 5877228, 84310620, 1184381844, 16385570076, 223935582828, 3030348558252, 40673437553748, 542180347359564, 7185077761974828, 94737850175764476, 1243661129422894356, 16262904060512571516, 211935250795961093868, 2753454797480878594380

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

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

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

Row 3 of A269201.

Empirical: a(n) = 24*a(n-1) -130*a(n-2) -248*a(n-3) +935*a(n-4) +272*a(n-5) -1768*a(n-6) +960*a(n-7) -144*a(n-8).

A269204 Number of 4Xn 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three no more than once.

Original entry on oeis.org

256, 15540, 471492, 15289548, 463790340, 13753913556, 399104835612, 11402099212308, 321701652077076, 8985658235129964, 248904744378939924, 6846738391062856596, 187219797100389992412, 5093241917191742737620

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Row 4 of A269201.

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

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

Cf. A269201.

Empirical: a(n) = 48*a(n-1) -424*a(n-2) -5664*a(n-3) +40624*a(n-4) +218356*a(n-5) -1300662*a(n-6) -2980700*a(n-7) +17916384*a(n-8) +2629424*a(n-9) -96328452*a(n-10) +132185980*a(n-11) -10936481*a(n-12) -91456900*a(n-13) +51588388*a(n-14) +9975760*a(n-15) -14279120*a(n-16) +2348160*a(n-17) +465152*a(n-18) -79872*a(n-19) -9216*a(n-20)

A269205 Number of 5 X n 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three no more than once.

Original entry on oeis.org

1024, 132300, 8314020, 555862380, 34838403756, 2135938293684, 128136007344516, 7568312936979972, 441444334269067260, 25489789190515708236, 1459585457554075237908, 82994548126187965994148

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Row 5 of A269201.

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 52

Cf. A269201.

Empirical recurrence of order 52 (see link above).

A269206 Number of 6Xn 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three no more than once.

Original entry on oeis.org

4096, 1090740, 142233732, 19558138380, 2532677348772, 320994710282892, 39825831571425924, 4865841496644992100, 587133256785089633172, 70137053123425124078748, 8308848756491598850682388

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Row 6 of A269201.

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

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

Cf. A269201.

cp's OEIS Frontend

A269196 Number of n X 3 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three no more than once.

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A269197 Number of n X 4 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three no more than once.

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A269198 Number of n X 5 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three no more than once.

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A269199 Number of nX6 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three no more than once.

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A269200 Number of n X 7 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three no more than once.

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A269202 Number of 2 X n 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three no more than once.

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A269203 Number of 3 X n 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three no more than once.

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A269204 Number of 4Xn 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three no more than once.

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A269205 Number of 5 X n 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three no more than once.

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A269206 Number of 6Xn 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three no more than once.

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