A269276 -id:A269276 - cp's OEIS frontend

A269269 Number of n X n 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three exactly once.

0, 108, 46872, 74853576, 542973139128, 19356924219624936, 3516906597130333936872, 3322606082327701612506093240, 16524782213263820847479975782463640

Offset: 1

R. H. Hardin, Feb 21 2016

nonn

Diagonal of A269276.

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

R. H. Hardin, Table of n, a(n) for n = 1..11

Cf. A269276.

A269270 Number of n X 2 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three exactly once.

Original entry on oeis.org

4, 108, 1620, 20412, 236196, 2598156, 27634932, 286978140, 2927177028, 29443957164, 292889889684, 2887057484028, 28242953648100, 274521509459532, 2653707924775476, 25530500379736476, 244598664928443012

Offset: 1

R. H. Hardin, Feb 21 2016

nonn

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

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

Column 2 of A269276.

Empirical: a(n) = 18*a(n-1) - 81*a(n-2).
Conjectures from Colin Barker, Jan 20 2019: (Start)
G.f.: 4*x*(1 + 9*x) / (1 - 9*x)^2.
a(n) = 9^(n-1) * (8*n-4).
(End)

A269271 Number of n X 3 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three exactly once.

Original entry on oeis.org

24, 1368, 46872, 1365336, 36673560, 938176344, 23230366488, 561939624792, 13356872620056, 313173275509080, 7262896745936664, 166932248829835608, 3808216985895026712, 86327991673633618776, 1946351959512905208600

Offset: 1

R. H. Hardin, Feb 21 2016

nonn

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

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

Column 3 of A269276.

Empirical: a(n) = 42*a(n-1) - 441*a(n-2).
Conjectures from Colin Barker, Jan 20 2019: (Start)
G.f.: 24*x*(1 + 15*x) / (1 - 21*x)^2.
a(n) = 8*3^n * 7^(n-2) * (12*n-5).
(End)

A269272 Number of n X 4 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three exactly once.

Original entry on oeis.org

108, 13896, 1104264, 74853576, 4684312584, 279339197256, 16128206816904, 909870855444936, 50443519266217224, 2758864964165996616, 149253876730080113544, 8002845140585293252296, 425920265748436386105864

Offset: 1

R. H. Hardin, Feb 21 2016

nonn

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

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

Column 4 of A269276.

Empirical: a(n) = 98*a(n-1) - 2401*a(n-2) for n > 3.
Conjectures from Colin Barker, Jan 20 2019: (Start)
G.f.: 36*x*(3 + 92*x + 49*x^2) / (1 - 49*x)^2.
a(n) = 72 * 49^(n-2) * (120*n-47) for n>1.
(End)

A269273 Number of n X 5 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three exactly once.

Original entry on oeis.org

432, 127512, 23549400, 3719884392, 542973139128, 75556007986536, 10181956012212600, 1340897428986116904, 173553231095580128184, 22161410569440812760552, 2799318884872209986120184

Offset: 1

R. H. Hardin, Feb 21 2016

nonn

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

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

Column 5 of A269276.

Empirical: a(n) = 234*a(n-1) - 14277*a(n-2) + 68796*a(n-3) - 86436*a(n-4).

Empirical g.f.: 72*x*(6 + 367*x - 1677*x^2 + 1302*x^3) / (1 - 117*x + 294*x^2)^2. - Colin Barker, Jan 21 2019

A269274 Number of nX6 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three exactly once.

Original entry on oeis.org

1620, 1104264, 474819408, 174924572760, 59587625651904, 19356924219624936, 6090616046325570480, 1872977567099580289656, 566116324214731470647712, 168820920854627863029497352, 49802534018235803452666079376

Offset: 1

R. H. Hardin, Feb 21 2016

nonn

Column 6 of A269276.

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

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

Cf. A269276.

Empirical: a(n) = 564*a(n-1) -87462*a(n-2) +2257724*a(n-3) -21169617*a(n-4) +76236552*a(n-5) -92236816*a(n-6) for n>7

A269275 Number of nX7 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three exactly once.

Original entry on oeis.org

5832, 9211608, 9230973192, 7934992835112, 6310088238337128, 4786284820998999528, 3516906597130333936872, 2525822328725627338344168, 1783069155917082001205203176, 1241926797984458949166277812968

Offset: 1

R. H. Hardin, Feb 21 2016

nonn

Column 7 of A269276.

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

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

Cf. A269276.

Empirical: a(n) = 1384*a(n-1) -566002*a(n-2) +61993580*a(n-3) -3083170217*a(n-4) +82564587476*a(n-5) -1288497445564*a(n-6) +12048887832352*a(n-7) -66380108132464*a(n-8) +198314583195456*a(n-9) -247475435747904*a(n-10) for n>11

A269277 Number of 2 X n 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three exactly once.

Original entry on oeis.org

0, 108, 1368, 13896, 127512, 1104264, 9211608, 74853576, 596581272, 4684312584, 36347893848, 279339197256, 2129701963032, 16128206816904, 121439499248088, 909870855444936, 6787656513072792, 50443519266217224, 373614100586474328

Offset: 1

R. H. Hardin, Feb 21 2016

nonn

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

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

Row 2 of A269276.

Empirical: a(n) = 14*a(n-1) - 49*a(n-2) for n>4.
Conjectures from Colin Barker, Jan 21 2019: (Start)
G.f.: 36*x^2*(3 - x)*(1 - x) / (1 - 7*x)^2.
a(n) = 72 * 7^(n-4) * (60*n-47) for n>2.
(End)

A269278 Number of 3 X n 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three exactly once.

Original entry on oeis.org

0, 1620, 46872, 1104264, 23549400, 474819408, 9230973192, 174918307032, 3252108138552, 59583135523968, 1078987217468328, 19354648265646120, 344454190256524824, 6089633274402902448, 107049250394211722184

Offset: 1

R. H. Hardin, Feb 21 2016

nonn

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

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

Row 3 of A269276.

Empirical: a(n) = 36*a(n-1) - 378*a(n-2) + 972*a(n-3) - 729*a(n-4) for n>7.

Empirical g.f.: 36*x^2*(45 - 318*x + 812*x^2 - 1698*x^3 + 2061*x^4 - 756*x^5) / (1 - 18*x + 27*x^2)^2. - Colin Barker, Jan 21 2019

A269279 Number of 4Xn 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three exactly once.

Original entry on oeis.org

0, 20412, 1365336, 74853576, 3719884392, 174924572760, 7934992835112, 350946381867480, 15232155757251048, 651580499598523992, 27551808205246504872, 1154085846201751972824, 47965168186749101620584

Offset: 1

R. H. Hardin, Feb 21 2016

nonn

Row 4 of A269276.

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

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

Cf. A269276.

Empirical: a(n) = 96*a(n-1) -3108*a(n-2) +40720*a(n-3) -265326*a(n-4) +931200*a(n-5) -1766452*a(n-6) +1678992*a(n-7) -622521*a(n-8) for n>12

cp's OEIS Frontend

A269269 Number of n X n 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three exactly once.

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A269270 Number of n X 2 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three exactly once.

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A269271 Number of n X 3 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three exactly once.

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A269272 Number of n X 4 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three exactly once.

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A269273 Number of n X 5 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three exactly once.

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A269274 Number of nX6 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three exactly once.

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A269275 Number of nX7 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three exactly once.

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A269277 Number of 2 X n 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three exactly once.

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A269278 Number of 3 X n 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three exactly once.

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A269279 Number of 4Xn 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three exactly once.

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