A269194 -id:A269194 - cp's OEIS frontend

A269188 Number of n X 2 0..3 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling three no more than once.

16, 108, 708, 4476, 27684, 168252, 1008804, 5983164, 35170980, 205214268, 1189853604, 6861684156, 39384946596, 225136169532, 1282284719268, 7279841963964, 41210177357988, 232678853273148, 1310648830057380

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

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

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

Column 2 of A269194.

Empirical: a(n) = 10*a(n-1) - 21*a(n-2) - 20*a(n-3) - 4*a(n-4) for n>5.

Empirical g.f.: 4*x*(4 - 13*x - 9*x^2 - 4*x^3 + 4*x^4) / (1 - 5*x - 2*x^2)^2. - Colin Barker, Jan 19 2019

A269189 Number of nX3 0..3 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling three no more than once.

Original entry on oeis.org

60, 708, 9284, 115452, 1399612, 16629436, 194596516, 2249848972, 25758552060, 292530733516, 3299601105860, 37002081127036, 412867979588732, 4586651556698652, 50758470773069860, 559808285415404076

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Column 3 of A269194.

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

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

Cf. A269194.

Empirical: a(n) = 22*a(n-1) -131*a(n-2) +88*a(n-3) +221*a(n-4) -154*a(n-5) -101*a(n-6) +44*a(n-7) -4*a(n-8) for n>9

A269190 Number of nX4 0..3 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling three no more than once.

Original entry on oeis.org

216, 4476, 115452, 2817548, 67134380, 1567933676, 36068275268, 819789099172, 18452018423420, 411983259384452, 9136178140885388, 201433537180523700, 4419013543755451812, 96521322466937887324, 2100165198065619059932

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Column 4 of A269194.

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

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

Cf. A269194.

Empirical: a(n) = 46*a(n-1) -607*a(n-2) +1264*a(n-3) +11029*a(n-4) -27640*a(n-5) -86627*a(n-6) +153412*a(n-7) +308464*a(n-8) -329306*a(n-9) -438615*a(n-10) +260680*a(n-11) +134834*a(n-12) -65824*a(n-13) -9889*a(n-14) +5080*a(n-15) -400*a(n-16) for n>17

A269191 Number of nX5 0..3 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling three no more than once.

Original entry on oeis.org

756, 27684, 1399612, 67134380, 3159954052, 145995171708, 6648192704604, 299224791093196, 13339889117822420, 590022908205332548, 25923065488446232140, 1132469284935764232244, 49229470523358865713156

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Column 5 of A269194.

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

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

Cf. A269194.

Empirical: a(n) = 118*a(n-1) -5041*a(n-2) +93278*a(n-3) -616456*a(n-4) -3048560*a(n-5) +60109885*a(n-6) -129687930*a(n-7) -1739169369*a(n-8) +8259890048*a(n-9) +20240706091*a(n-10) -173579758748*a(n-11) -34263378926*a(n-12) +1854959811756*a(n-13) -1352133363698*a(n-14) -11158815731728*a(n-15) +13195242387667*a(n-16) +40081045519402*a(n-17) -56960114535700*a(n-18) -88448187207398*a(n-19) +137934077935370*a(n-20) +119462198991804*a(n-21) -202996386004581*a(n-22) -94913498792266*a(n-23) +187975033925075*a(n-24) +38342927037264*a(n-25) -110576189373568*a(n-26) -1510870946200*a(n-27) +40619114535308*a(n-28) -5466962964240*a(n-29) -8777770697408*a(n-30) +2325318442944*a(n-31) +946747193728*a(n-32) -404404766528*a(n-33) -21593127872*a(n-34) +28030228480*a(n-35) -2948913408*a(n-36) -308060672*a(n-37) +51977984*a(n-38) +752640*a(n-39) -230400*a(n-40) for n>41

A269192 Number of nX6 0..3 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling three no more than once.

Original entry on oeis.org

2592, 168252, 16629436, 1567933676, 145995171708, 13377149358556, 1209655310225276, 108189166610803900, 9588279038550679252, 843282890295576773948, 73686476215233408557636, 6403039770601949503501428

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Column 6 of A269194.

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

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

Cf. A269194.

A269193 Number of nX7 0..3 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling three no more than once.

Original entry on oeis.org

8748, 1008804, 194596516, 36068275268, 6648192704604, 1209655310225276, 217602949665911156, 38754403905072091620, 6843294057789444736828, 1199620248489898735000620, 208983050480777152531950868

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Column 7 of A269194.

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

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

Cf. A269194.

A269187 Number of n X n 0..3 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling three no more than once.

Original entry on oeis.org

4, 108, 9284, 2817548, 3159954052, 13377149358556, 217602949665911156, 13760950074226562086140, 3411379570274317633099847884, 3335382860394625859139269051079788

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Diagonal of A269194.

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

Cf. A269194.

cp's OEIS Frontend

A269188 Number of n X 2 0..3 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling three no more than once.

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A269189 Number of nX3 0..3 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling three no more than once.

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A269190 Number of nX4 0..3 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling three no more than once.

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A269191 Number of nX5 0..3 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling three no more than once.

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A269192 Number of nX6 0..3 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling three no more than once.

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A269193 Number of nX7 0..3 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling three no more than once.

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A269187 Number of n X n 0..3 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling three no more than once.

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