A231753 -id:A231753 - cp's OEIS frontend

A231747 Number of n X 2 0..2 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors.

3, 15, 51, 186, 687, 2485, 9068, 33308, 121445, 444183, 1626731, 5949198, 21774916, 79713938, 291767058, 1068145321, 3910543065, 14316731138, 52417430039, 191916565888, 702674552025, 2572785049162, 9420099176524, 34491356066515

Offset: 1

R. H. Hardin, Nov 13 2013

nonn

			Some solutions for n=7:
..1..0....2..2....0..2....0..0....1..0....2..1....0..0....0..0....2..0....0..2
..0..0....1..1....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0
..0..0....1..1....0..0....0..0....0..0....0..0....0..1....1..2....0..0....0..0
..0..0....1..1....2..1....1..1....0..0....0..0....0..0....1..1....0..2....0..1
..1..2....2..1....0..0....2..1....1..1....0..0....0..0....1..2....0..0....0..2
..1..1....2..1....0..0....1..1....1..1....2..0....2..1....1..1....0..0....0..0
..1..1....1..1....1..0....1..2....1..1....0..0....1..1....1..2....0..2....0..2

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

Column 2 of A231753.

Empirical: a(n) = 3*a(n-1) + 3*a(n-2) + 14*a(n-3) - 39*a(n-4) - 45*a(n-5) - 124*a(n-6) + 18*a(n-7) + 132*a(n-8) + 248*a(n-9) + 112*a(n-10) + 64*a(n-11).

Empirical g.f.: x*(3 + 6*x - 3*x^2 - 54*x^3 - 117*x^4 - 128*x^5 - 16*x^6 + 386*x^7 + 348*x^8 + 224*x^9 + 64*x^10) / (1 - 3*x - 3*x^2 - 14*x^3 + 39*x^4 + 45*x^5 + 124*x^6 - 18*x^7 - 132*x^8 - 248*x^9 - 112*x^10 - 64*x^11). - Colin Barker, Sep 30 2018

A231748 Number of nX3 0..2 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors.

Original entry on oeis.org

9, 51, 589, 5106, 41288, 397219, 3745096, 34036486, 313782748, 2927905037, 27164864918, 251564198963, 2335778916642, 21695352159535, 201366887006680, 1869228803618176, 17356005419910937, 161143681489604094

Offset: 1

R. H. Hardin, Nov 13 2013

nonn

Column 3 of A231753

			Some solutions for n=5
..0..0..0....0..1..1....2..0..0....2..0..0....0..0..0....0..0..2....0..1..2
..1..0..1....0..0..0....2..0..0....0..0..2....0..0..0....1..0..0....0..0..1
..0..2..2....2..0..0....0..1..1....0..0..2....0..2..2....1..1..0....0..0..2
..0..0..1....0..0..2....0..0..1....0..0..1....2..0..2....2..0..2....2..0..1
..2..0..0....0..1..1....0..0..1....1..0..0....0..0..0....0..0..0....0..0..0

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

Empirical: a(n) = 9*a(n-1) -10*a(n-2) +205*a(n-3) -343*a(n-4) -3172*a(n-5) -8106*a(n-6) -19608*a(n-7) -86820*a(n-8) +105508*a(n-9) -250613*a(n-10) +525498*a(n-11) +3710627*a(n-12) +6249063*a(n-13) +11770795*a(n-14) -927423*a(n-15) -28037328*a(n-16) -60164511*a(n-17) -139179633*a(n-18) -217274117*a(n-19) -213592727*a(n-20) -140322482*a(n-21) +154891348*a(n-22) +398534065*a(n-23) +772218755*a(n-24) +811574834*a(n-25) +702028305*a(n-26) +477484534*a(n-27) -54847598*a(n-28) -371753704*a(n-29) -646008553*a(n-30) -754680367*a(n-31) -605925622*a(n-32) -423754908*a(n-33) -245157008*a(n-34) -118738252*a(n-35) -48930960*a(n-36) -12367856*a(n-37) -4600192*a(n-38) -2156032*a(n-39) -279552*a(n-40) for n>41

A231749 Number of nX4 0..2 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors.

Original entry on oeis.org

22, 186, 5106, 101517, 1787168, 36596191, 764681711, 15421779553, 309633476778, 6284893573378, 127697430555401, 2587148736974819, 52408991398868709, 1062536884554302876, 21542235015238071587, 436659223538195787389

Offset: 1

R. H. Hardin, Nov 13 2013

nonn

Column 4 of A231753

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

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

A231750 Number of nX5 0..2 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors.

Original entry on oeis.org

51, 687, 41288, 1787168, 67411714, 2966010838, 131956285636, 5669387332934, 243573416110820, 10555475178328001, 457172040211929179, 19760692150060588600, 854390327504135396722, 36958540950287007144750

Offset: 1

R. H. Hardin, Nov 13 2013

nonn

Column 5 of A231753

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

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

A231751 Number of nX6 0..2 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors.

Original entry on oeis.org

121, 2485, 397219, 36596191, 2966010838, 309458955366, 31638510266609, 3041193156650724, 296576264769131499, 29380275874994459363, 2892477394704091137503, 283798285900590449754004

Offset: 1

R. H. Hardin, Nov 13 2013

nonn

Column 6 of A231753

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

R. H. Hardin, Table of n, a(n) for n = 1..149

A231752 Number of nX7 0..2 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors.

Original entry on oeis.org

292, 9068, 3745096, 764681711, 131956285636, 31638510266609, 7467132505589749, 1615073569445439856, 354430510983036028174, 79728003072248618902703, 17808572706541641197645512, 3952770212213173521620797011

Offset: 1

R. H. Hardin, Nov 13 2013

nonn

Column 7 of A231753

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

R. H. Hardin, Table of n, a(n) for n = 1..26

cp's OEIS Frontend

A231747 Number of n X 2 0..2 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors.

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A231748 Number of nX3 0..2 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors.

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A231749 Number of nX4 0..2 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors.

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A231750 Number of nX5 0..2 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors.

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A231751 Number of nX6 0..2 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors.

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A231752 Number of nX7 0..2 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors.

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