A269214 -id:A269214 - cp's OEIS frontend

A269212 Number of nX6 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three exactly once.

1620, 360960, 70371048, 11985002256, 1910809190712, 292321215814512, 43468685827935816, 6331185189881558208, 907653167033915932536, 128509758210816109187040, 18012346515317443065043752

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Column 6 of A269214.

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

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

Cf. A269214.

Empirical recurrence of order 42 (see link above)

A269215 Number of 2 X n 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three exactly once.

Original entry on oeis.org

0, 96, 768, 6528, 49536, 360960, 2546304, 17563392, 119091072, 796813824, 5274483840, 34608512256, 225420724608, 1459142258688, 9394561013376, 60205610853120, 384263133750144, 2443755614295552, 15491594556534912

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Row 2 of A269214.

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

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

Cf. A269214.

Empirical: a(n) = 10*a(n-1) - 13*a(n-2) - 60*a(n-3) - 36*a(n-4).
From Colin Barker, Mar 21 2018: (Start)
G.f.: 96*x^2*(1 - x)^2 / ((1 + x)^2*(1 - 6*x)^2).
a(n) = 8*(175*6^n*n + 1008*n - 55*6^n - 288) / 1029 for n even.
a(n) = 8*(175*6^n*n - 1008*n - 55*6^n + 288) / 1029 for n odd.
(End)

A269209 Number of n X 3 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three exactly once.

Original entry on oeis.org

24, 768, 18048, 361728, 6712704, 118872576, 2039727744, 34214296320, 564168820608, 9179147971584, 147751571802240, 2357407757843712, 37337046775523712, 587670598254177792, 9200252201653201536

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

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

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

Column 3 of A269214.

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.: 24*x*(1 + 2*x + 29*x^2 - 84*x^3 + 36*x^4) / (1 - 15*x + 6*x^2)^2. - Colin Barker, Jan 20 2019

A269210 Number of n X 4 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three exactly once.

Original entry on oeis.org

108, 6528, 308544, 12548544, 474091776, 17118725376, 599456856000, 20531285093184, 691495131961728, 22985647571590272, 756022683316823616, 24651356966323488960, 797979183054277922304, 25672248307708057755648

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

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

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

Column 4 of A269214.

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*(9 - 14*x + 1263*x^2 - 7188*x^3 + 10471*x^4 - 4926*x^5 + 897*x^6) / ((1 - x)^2*(1 - 30*x + 5*x^2)^2). - Colin Barker, Jan 20 2019

A269211 Number of nX5 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three exactly once.

Original entry on oeis.org

432, 49536, 4744704, 394072704, 30541426560, 2267772823680, 163535201141376, 11544796423498368, 801929439109544064, 54999867607734747264, 3733606080456064161408, 251316480848067823807104

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Column 5 of A269214.

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

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

Cf. A269214.

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

A269213 Number of nX7 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three exactly once.

Original entry on oeis.org

5832, 2546304, 1012764384, 354189986208, 116322554833728, 36713945487331392, 11273191243423937904, 3392211859561264876416, 1005065652737890110097824, 294164506851983123928014976, 85246917739611183231260455872

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Column 7 of A269214.

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

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

Cf. A269214.

A269216 Number of 3Xn 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three exactly once.

Original entry on oeis.org

0, 1152, 18048, 308544, 4744704, 70371048, 1012764384, 14272781904, 197924795136, 2710127012280, 36731155605600, 493646491209600, 6587572246924800, 87381895621488648, 1153101183028855008

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Row 3 of A269214.

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

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

Cf. A269214.

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)

A269217 Number of 4Xn 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three exactly once.

Original entry on oeis.org

0, 11424, 361728, 12548544, 394072704, 11985002256, 354189986208, 10261769266944, 292749231337728, 8250573640526208, 230241360762467712, 6372885696329678304, 175188945893347242144, 4787785430572600575216

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Row 4 of A269214.

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

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

Cf. A269214.

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)

A269218 Number of 5Xn 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three exactly once.

Original entry on oeis.org

0, 103488, 6712704, 474091776, 30541426560, 1910809190712, 116322554833728, 6948456736101264, 408916976890552416, 23782890276972969552, 1370013927382609217472, 78294173211595616892096

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Row 5 of A269214.

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

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

Cf. A269214.

Empirical recurrence of order 52 (see link above)

A269219 Number of 6Xn 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three exactly once.

Original entry on oeis.org

0, 889056, 118872576, 17118725376, 2267772823680, 292321215814512, 36713945487331392, 4528086446983948224, 550465224463202188320, 66156064863501806179776, 7876627077577027391888640

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Row 6 of A269214.

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

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

Cf. A269214.

cp's OEIS Frontend

A269212 Number of nX6 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three exactly once.

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A269215 Number of 2 X n 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three exactly once.

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A269209 Number of n X 3 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three exactly once.

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A269210 Number of n X 4 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three exactly once.

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A269211 Number of nX5 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three exactly once.

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A269213 Number of nX7 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three exactly once.

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A269216 Number of 3Xn 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three exactly once.

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A269217 Number of 4Xn 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three exactly once.

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A269218 Number of 5Xn 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three exactly once.

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A269219 Number of 6Xn 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three exactly once.