A231382 -id:A231382 - cp's OEIS frontend

A231376 Number of n X 2 0..1 arrays with no element less than a strict majority of its horizontal and vertical neighbors.

2, 10, 21, 48, 113, 261, 601, 1390, 3216, 7435, 17190, 39751, 91921, 212555, 491510, 1136570, 2628207, 6077470, 14053561, 32497507, 75147355, 173771026, 401828790, 929190453, 2148663614, 4968578109, 11489359399, 26568039511, 61436038272

Offset: 1

R. H. Hardin, Nov 08 2013

nonn

Column 2 of A231382.

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

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

Cf. A231382.

Empirical: a(n) = 3*a(n-1) - 2*a(n-2) + 2*a(n-3) - 2*a(n-4) - a(n-5) for n>6.

Empirical g.f.: x*(2 + 4*x - 5*x^2 + x^3 - 5*x^4 - 2*x^5) / (1 - 3*x + 2*x^2 - 2*x^3 + 2*x^4 + x^5). - Colin Barker, Mar 18 2018

A231377 Number of n X 3 0..1 arrays with no element less than a strict majority of its horizontal and vertical neighbors.

Original entry on oeis.org

4, 21, 93, 378, 1519, 6126, 24747, 99964, 403743, 1630662, 6586087, 26600572, 107437031, 433927396, 1752589551, 7078534592, 28589495207, 115470119764, 466372299261, 1883631211124, 7607798625811, 30727139997676, 124103854340837

Offset: 1

R. H. Hardin, Nov 08 2013

nonn

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

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

Column 3 of A231382.

Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 16*a(n-3) - 14*a(n-4) - 3*a(n-5) + 8*a(n-6) - 9*a(n-7) - 2*a(n-8) + 6*a(n-9) + 2*a(n-10) for n>11.

Empirical g.f.: x*(4 - 3*x + 11*x^2 - 13*x^3 - 6*x^4 - 12*x^5 - 15*x^6 + 3*x^7 + 13*x^8 + 8*x^9 + 2*x^10) / (1 - 6*x + 11*x^2 - 16*x^3 + 14*x^4 + 3*x^5 - 8*x^6 + 9*x^7 + 2*x^8 - 6*x^9 - 2*x^10). - Colin Barker, Sep 28 2018

A231378 Number of nX4 0..1 arrays with no element less than a strict majority of its horizontal and vertical neighbors.

Original entry on oeis.org

7, 48, 378, 2539, 17363, 120124, 830890, 5746499, 39745115, 274872588, 1900931060, 13146313579, 90916738809, 628758673194, 4348344850906, 30072109222833, 207971483025113, 1438280832129012, 9946804915649296, 68789714754091787

Offset: 1

R. H. Hardin, Nov 08 2013

nonn

Column 4 of A231382

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

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

Empirical: a(n) = 10*a(n-1) -31*a(n-2) +82*a(n-3) -131*a(n-4) +226*a(n-5) -319*a(n-6) +206*a(n-7) -574*a(n-8) +483*a(n-9) -432*a(n-10) +517*a(n-11) +132*a(n-12) +746*a(n-13) -145*a(n-14) -228*a(n-15) -6*a(n-16) +41*a(n-17) +3*a(n-18) -3*a(n-19) for n>20

A231379 Number of nX5 0..1 arrays with no element less than a strict majority of its horizontal and vertical neighbors.

Original entry on oeis.org

12, 113, 1519, 17363, 209118, 2547810, 30936914, 375620622, 4560995236, 55375119088, 672313654008, 8162807379715, 99107740379983, 1203301841913136, 14609703508465925, 177381467975127821, 2153649923765174964

Offset: 1

R. H. Hardin, Nov 08 2013

nonn

Column 5 of A231382

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

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

Empirical: a(n) = 21*a(n-1) -168*a(n-2) +988*a(n-3) -4019*a(n-4) +14018*a(n-5) -38338*a(n-6) +76250*a(n-7) -75318*a(n-8) -25048*a(n-9) -2704*a(n-10) +284955*a(n-11) -215394*a(n-12) -880505*a(n-13) -242350*a(n-14) +5521214*a(n-15) +653795*a(n-16) -10478457*a(n-17) -9279936*a(n-18) +15930956*a(n-19) +21911876*a(n-20) -8411513*a(n-21) -37124626*a(n-22) -3849041*a(n-23) +23286499*a(n-24) -8400505*a(n-25) -9905859*a(n-26) +47524429*a(n-27) +20129245*a(n-28) -116149038*a(n-29) +2411219*a(n-30) +172063757*a(n-31) -3388918*a(n-32) -136545864*a(n-33) -28219012*a(n-34) +67852922*a(n-35) +54667307*a(n-36) +2102952*a(n-37) -12764701*a(n-38) -5492419*a(n-39) -787424*a(n-40) +318583*a(n-41) +347059*a(n-42) +193761*a(n-43) +39772*a(n-44) -696*a(n-45) -1216*a(n-46) for n>47

A231380 Number of nX6 0..1 arrays with no element less than a strict majority of its horizontal and vertical neighbors.

Original entry on oeis.org

21, 261, 6126, 120124, 2547810, 54485279, 1157805351, 24615811883, 523548909308, 11133382117666, 236751472446562, 5034642562404119, 107064153494511600, 2276766498890520783, 48416455811053263714, 1029597712238409457187

Offset: 1

R. H. Hardin, Nov 08 2013

nonn

Column 6 of A231382

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

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

A231381 Number of nX7 0..1 arrays with no element less than a strict majority of its horizontal and vertical neighbors.

Original entry on oeis.org

37, 601, 24747, 830890, 30936914, 1157805351, 42978519280, 1597438228604, 59402875813957, 2208383979206654, 82098126041989007, 3052145959217113535, 113469026790211137424, 4218406116270705640956, 156826531286247105951370

Offset: 1

R. H. Hardin, Nov 08 2013

nonn

Column 7 of A231382

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

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

A231375 Number of n X n 0..1 arrays with no element less than a strict majority of its horizontal and vertical neighbors.

Original entry on oeis.org

2, 10, 93, 2539, 209118, 54485279, 42978519280, 103861521149940, 768825093368064218, 17400837260687664224580, 1205024418040758639132121433, 255358434130512785761464119154485

Offset: 1

R. H. Hardin, Nov 08 2013

nonn

Diagonal of A231382

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

cp's OEIS Frontend

A231376 Number of n X 2 0..1 arrays with no element less than a strict majority of its horizontal and vertical neighbors.

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A231377 Number of n X 3 0..1 arrays with no element less than a strict majority of its horizontal and vertical neighbors.

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A231378 Number of nX4 0..1 arrays with no element less than a strict majority of its horizontal and vertical neighbors.

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A231379 Number of nX5 0..1 arrays with no element less than a strict majority of its horizontal and vertical neighbors.

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A231380 Number of nX6 0..1 arrays with no element less than a strict majority of its horizontal and vertical neighbors.

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A231381 Number of nX7 0..1 arrays with no element less than a strict majority of its horizontal and vertical neighbors.

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A231375 Number of n X n 0..1 arrays with no element less than a strict majority of its horizontal and vertical neighbors.

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