A269186 -id:A269186 - cp's OEIS frontend

A269180 Number of n X 2 0..3 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling three exactly once.

4, 48, 384, 2736, 18336, 118032, 739008, 4533744, 27384288, 163381968, 965118720, 5654345136, 32898781728, 190290667152, 1095084877632, 6274151751024, 35807326610016, 203653219107408, 1154714957732736, 6529188836867376

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

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

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

Column 2 of A269186.

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*(1 - x)^2*(1 + 2*x)^2 / (1 - 5*x - 2*x^2)^2. - Colin Barker, Jan 19 2019

A269181 Number of nX3 0..3 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling three exactly once.

Original entry on oeis.org

24, 384, 5888, 80112, 1031344, 12791896, 154606864, 1833130768, 21416076480, 247279304248, 2828051682752, 32088228414160, 361662427633424, 4053056289550296, 45198059875209904, 501865175240768976

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Column 3 of A269186.

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

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

Cf. A269186.

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

A269182 Number of nX4 0..3 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling three exactly once.

Original entry on oeis.org

108, 2736, 80112, 2097552, 52394312, 1265974992, 29881402560, 693021071760, 15854541802056, 358760880894864, 8045649521280080, 179088561311942528, 3961164069598726264, 87139967884594089296, 1907940856141713336608

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Column 4 of A269186.

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

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

Cf. A269186.

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

A269183 Number of nX5 0..3 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling three exactly once.

Original entry on oeis.org

432, 18336, 1031344, 52394312, 2563440512, 121792778352, 5665397992608, 259306140235672, 11718368891185840, 524154208020159720, 23247356088445416368, 1023776741213223461792, 44814164049516781057936

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Column 5 of A269186.

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

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

Cf. A269186.

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

A269184 Number of nX6 0..3 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling three exactly once.

Original entry on oeis.org

1620, 118032, 12791896, 1265974992, 121792778352, 11426543880704, 1052109184130840, 95454531912315856, 8558619944786977592, 760020559893342078688, 66953271981144607663880, 5858534813761786497448832

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Column 6 of A269186.

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

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

Cf. A269186.

A269185 Number of nX7 0..3 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling three exactly once.

Original entry on oeis.org

5832, 739008, 154606864, 29881402560, 5665397992608, 1052109184130840, 192247800095048896, 34666986301328823344, 6183899646434421899984, 1093211509437280016564192, 191809173606551182685393776

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Column 7 of A269186.

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

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

Cf. A269186.

A269179 Number of n X n 0..3 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling three exactly once.

Original entry on oeis.org

0, 48, 5888, 2097552, 2563440512, 11426543880704, 192247800095048896, 12445275374147703433760, 3138050414883209885285902752, 3107560086436286975829696986907248

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Diagonal of A269186.

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

Cf. A269186.

cp's OEIS Frontend

A269180 Number of n X 2 0..3 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling three exactly once.

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A269181 Number of nX3 0..3 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling three exactly once.

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A269182 Number of nX4 0..3 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling three exactly once.

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A269183 Number of nX5 0..3 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling three exactly once.

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A269184 Number of nX6 0..3 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling three exactly once.

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A269185 Number of nX7 0..3 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling three exactly once.

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Examples

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A269179 Number of n X n 0..3 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling three exactly once.

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