A231324 -id:A231324 - cp's OEIS frontend

A231317 Number of (n+1) X (1+1) 0..2 arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

6, 24, 216, 1536, 11616, 86400, 645504, 4816896, 35956224, 268376064, 2003195904, 14952038400, 111603572736, 833020329984, 6217748545536, 46409906651136, 346408259813376, 2585626450329600, 19299378566529024, 144052522724622336

Offset: 1

R. H. Hardin, Nov 07 2013

nonn

Column 1 of A231324.

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

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

Cf. A231324.

Empirical: a(n) = 6*a(n-1) + 12*a(n-2) - 8*a(n-3).
Conjectures from Colin Barker, Mar 18 2018: (Start)
G.f.: 6*x*(1 - 2*x) / ((1 + 2*x)*(1 - 8*x + 4*x^2)).
a(n) = ((-2)^(1+n) + (4-2*sqrt(3))^n + (2*(2+sqrt(3)))^n) / 2.
(End)

A231318 Number of (n+1) X (2+1) 0..2 arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

24, 432, 9600, 192192, 3917184, 79306752, 1607468544, 32569451520, 659942375424, 13371898245120, 270945239064576, 5489964932136960, 111239155883802624, 2253957795356147712, 45670301427851329536, 925383976903713226752

Offset: 1

R. H. Hardin, Nov 07 2013

nonn

Column 2 of A231324.

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

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

Cf. A231324.

Empirical: a(n) = 22*a(n-1) -776*a(n-3) +944*a(n-4) +7168*a(n-5) -12416*a(n-6) +9216*a(n-8) -4096*a(n-9).

A231319 Number of (n+1)X(3+1) 0..2 arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

216, 9600, 569184, 30645600, 1695860064, 93216760416, 5132640060000, 282526545904224, 15552808745472864, 856159949131740000, 47130503963700361056, 2594473391280336234336, 142822425161120289404256

Offset: 1

R. H. Hardin, Nov 07 2013

nonn

Column 3 of A231324

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

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

Empirical: a(n) = 57*a(n-1) +194*a(n-2) -16272*a(n-3) -50654*a(n-4) +1754012*a(n-5) +5241944*a(n-6) -96475568*a(n-7) -98407584*a(n-8) +2319538080*a(n-9) +20230624*a(n-10) -29255162752*a(n-11) +17323897856*a(n-12) +225620671744*a(n-13) -258160872704*a(n-14) -1110522717184*a(n-15) +2032863418368*a(n-16) +3190512078848*a(n-17) -9576311832576*a(n-18) -4024700600320*a(n-19) +29553678188544*a(n-20) -5539096297472*a(n-21) -61959824474112*a(n-22) +34977239007232*a(n-23) +85185755348992*a(n-24) -68609208483840*a(n-25) -75467489017856*a(n-26) +75009850605568*a(n-27) +41280625180672*a(n-28) -51374922399744*a(n-29) -11009074921472*a(n-30) +21444771708928*a(n-31) -498216206336*a(n-32) -4492535791616*a(n-33) +747324309504*a(n-34) +309237645312*a(n-35) -68719476736*a(n-36)

A231320 Number of (n+1)X(4+1) 0..2 arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

1536, 192192, 30645600, 4509951264, 677392128096, 101255199764448, 15154743446853216, 2267704492520687136, 339353240593608062304, 50782606894918838006496, 7599400278857398619862624

Offset: 1

R. H. Hardin, Nov 07 2013

nonn

Column 4 of A231324

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 81

Empirical recurrence of order 81 (see link above)

A231321 Number of (n+1)X(5+1) 0..2 arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

11616, 3917184, 1695860064, 677392128096, 277024322215296, 112717970818679904, 45929855692690790400, 18711513985409981683296, 7623482985272651235333504, 3105964603406107757886555744

Offset: 1

R. H. Hardin, Nov 07 2013

nonn

Column 5 of A231324

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

R. H. Hardin, Table of n, a(n) for n = 1..51

A231322 Number of (n+1)X(6+1) 0..2 arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

86400, 79306752, 93216760416, 101255199764448, 112717970818679904, 124848872383160454816, 138493610465688295961184, 153600875343463960773850752, 170368502364235084980055819776

Offset: 1

R. H. Hardin, Nov 07 2013

nonn

Column 6 of A231324

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

R. H. Hardin, Table of n, a(n) for n = 1..21

A231323 Number of (n+1) X (7+1) 0..2 arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

645504, 1607468544, 5132640060000, 15154743446853216, 45929855692690790400, 138493610465688295961184, 418284029768568825937161600, 1263090712888488868089057630816, 3814456862436895259545489736740704

Offset: 1

R. H. Hardin, Nov 07 2013

nonn

Column 7 of A231324.

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

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

Cf. A231324.

A231316 Number of (n+1)X(n+1) 0..2 arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

6, 432, 569184, 4509951264, 277024322215296, 124848872383160454816, 418284029768568825937161600, 10384840669528137933211181787934080, 1911676181020982254709223663612649499528544

Offset: 1

R. H. Hardin, Nov 07 2013

nonn

Diagonal of A231324

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

cp's OEIS Frontend

A231317 Number of (n+1) X (1+1) 0..2 arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

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A231318 Number of (n+1) X (2+1) 0..2 arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

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A231319 Number of (n+1)X(3+1) 0..2 arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

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A231320 Number of (n+1)X(4+1) 0..2 arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

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A231321 Number of (n+1)X(5+1) 0..2 arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

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A231322 Number of (n+1)X(6+1) 0..2 arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

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A231323 Number of (n+1) X (7+1) 0..2 arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

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A231316 Number of (n+1)X(n+1) 0..2 arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

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