A269152 -id:A269152 - cp's OEIS frontend

A269146 Number of n X 2 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three exactly once.

4, 80, 768, 6224, 46464, 330192, 2270592, 15251152, 100647168, 655139152, 4217820672, 26911075152, 170416738944, 1072338720464, 6710943646848, 41800542176720, 259288295447040, 1602497927690832, 9871915467776256

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

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

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

Column 2 of A269152.

Empirical: a(n) = 12*a(n-1) - 38*a(n-2) + 12*a(n-3) - a(n-4) for n>5.

Empirical g.f.: 4*x*(1 - x)*(1 + 9*x - x^2 - x^3) / (1 - 6*x + x^2)^2. - Colin Barker, Jan 19 2019

A269147 Number of nX3 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three exactly once.

Original entry on oeis.org

24, 768, 13904, 220968, 3277728, 46576336, 642676704, 8680278136, 115349343264, 1513379596864, 19651887694240, 253030595298696, 3234828051983328, 41105657832397744, 519625334069189984, 6539008095907322520

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Column 3 of A269152.

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

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

Cf. A269152.

Empirical: a(n) = 26*a(n-1) -199*a(n-2) +408*a(n-3) -463*a(n-4) +322*a(n-5) -141*a(n-6) +36*a(n-7) -4*a(n-8) for n>9

A269148 Number of nX4 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three exactly once.

Original entry on oeis.org

108, 6224, 220968, 7002040, 208984848, 6004186984, 167970539096, 4607603633440, 124496158984840, 3323815506994632, 87881068225023056, 2304923699010954504, 60044569367490800584, 1555171706058316642096, 40078683916858034569112

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Column 4 of A269152.

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

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

Cf. A269152.

Empirical: a(n) = 58*a(n-1) -1093*a(n-2) +7680*a(n-3) -27078*a(n-4) +58958*a(n-5) -88914*a(n-6) +82212*a(n-7) -35159*a(n-8) -20796*a(n-9) +39556*a(n-10) -11364*a(n-11) -13593*a(n-12) +9618*a(n-13) +429*a(n-14) -2060*a(n-15) +434*a(n-16) +166*a(n-17) -92*a(n-18) +16*a(n-19) -a(n-20) for n>22

A269149 Number of nX5 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three exactly once.

Original entry on oeis.org

432, 46464, 3277728, 208984848, 12637025328, 738478504448, 42119837369168, 2359047063894464, 130272136732736736, 7113223023541150960, 384838349955877213536, 20661359894841380480272, 1102107089173705118234384

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Column 5 of A269152.

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

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

Cf. A269152.

Empirical: a(n) = 134*a(n-1) -6403*a(n-2) +137212*a(n-3) -1537987*a(n-4) +10006762*a(n-5) -41364815*a(n-6) +107588656*a(n-7) -111196320*a(n-8) -399050332*a(n-9) +2108507944*a(n-10) -4098003684*a(n-11) +445179883*a(n-12) +18009896226*a(n-13) -42207232033*a(n-14) +12581717548*a(n-15) +122544940860*a(n-16) -203283873760*a(n-17) -79843687188*a(n-18) +508551706160*a(n-19) -240288894385*a(n-20) -648319426210*a(n-21) +662670918703*a(n-22) +480938145704*a(n-23) -858808887300*a(n-24) -176689259732*a(n-25) +734283407564*a(n-26) -39751157620*a(n-27) -450104705459*a(n-28) +101139044518*a(n-29) +200718146529*a(n-30) -72282159428*a(n-31) -63674380919*a(n-32) +31546829386*a(n-33) +13183985923*a(n-34) -9057688788*a(n-35) -1275648164*a(n-36) +1571020336*a(n-37) -67398016*a(n-38) -125671104*a(n-39) +17151168*a(n-40) +3564288*a(n-41) -665856*a(n-42) for n>45

A269150 Number of nX6 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three exactly once.

Original entry on oeis.org

1620, 330192, 46576336, 6004186984, 738478504448, 88082672552208, 10275566914040000, 1178661175005532168, 133416857282270562320, 14941436920498380518848, 1658672032118594665963168

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Column 6 of A269152.

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

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

Cf. A269152.

A269151 Number of n X 7 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three exactly once.

Original entry on oeis.org

5832, 2270592, 642676704, 167970539096, 42119837369168, 10275566914040000, 2456638851763181776, 578202261783376052264, 134401513805944458613328, 30926068491391277680083776, 7056680383368519798619918656

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Column 7 of A269152.

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

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

Cf. A269152.

A269145 Number of n X n 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three exactly once.

Original entry on oeis.org

0, 80, 13904, 7002040, 12637025328, 88082672552208, 2456638851763181776, 279573979783982763379528, 131383670545605944288719844352, 256961574793195204388371517319842144

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Diagonal of A269152.

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

Cf. A269152.

cp's OEIS Frontend

A269146 Number of n X 2 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three exactly once.

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A269147 Number of nX3 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three exactly once.

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A269148 Number of nX4 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three exactly once.

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A269149 Number of nX5 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three exactly once.

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A269150 Number of nX6 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three exactly once.

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A269151 Number of n X 7 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three exactly once.

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A269145 Number of n X n 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three exactly once.

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