A231396 -id:A231396 - cp's OEIS frontend

A231390 Number of (n+1) X (2+1) 0..2 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

7, 8, 15, 20, 31, 52, 95, 180, 351, 692, 1375, 2740, 5471, 10932, 21855, 43700, 87391, 174772, 349535, 699060, 1398111, 2796212, 5592415, 11184820, 22369631, 44739252, 89478495, 178956980, 357913951, 715827892, 1431655775, 2863311540, 5726623071

Offset: 1

R. H. Hardin, Nov 08 2013

nonn

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

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

Column 2 of A231396.

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

Empirical g.f.: x*(7 - 6*x - 8*x^2 - 4*x^3 - 8*x^4) / ((1 - x)*(1 + x)*(1 - 2*x)). - Colin Barker, Sep 28 2018

A231391 Number of (n+1) X (3+1) 0..2 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

14, 38, 100, 272, 740, 2061, 5834, 16521, 46969, 133864, 382377, 1093837, 3133209, 8984580, 25782696, 74034161, 212690121, 611260183, 1757248511, 5052897615, 14532031920, 41799692849, 120245136990, 345938696990, 995313138719

Offset: 1

R. H. Hardin, Nov 08 2013

nonn

Column 3 of A231396.

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

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

Cf. A231396.

Empirical: a(n) = 4*a(n-1) -8*a(n-3) -8*a(n-4) +7*a(n-5) +12*a(n-6) +23*a(n-7) -42*a(n-8) -16*a(n-9) +81*a(n-10) -14*a(n-11) -52*a(n-12) +15*a(n-13) -2*a(n-14) -17*a(n-15) +4*a(n-16) +10*a(n-17) +4*a(n-18).

A231392 Number of (n+1)X(4+1) 0..2 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

33, 90, 311, 1096, 4085, 15732, 62039, 245850, 980361, 3915982, 15667453, 62726276, 251241863, 1006595336, 4033439213, 16163623302, 64777551551, 259612134798, 1040482017255, 4170131147952, 16713541804781, 66986842603436

Offset: 1

R. H. Hardin, Nov 08 2013

nonn

Column 4 of A231396

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

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

Empirical: a(n) = 6*a(n-1) -2*a(n-2) -28*a(n-3) -5*a(n-4) +74*a(n-5) +67*a(n-6) -29*a(n-7) -322*a(n-8) +13*a(n-9) +804*a(n-10) -816*a(n-11) +389*a(n-12) -306*a(n-13) -903*a(n-14) +1630*a(n-15) -942*a(n-16) +736*a(n-17) -1009*a(n-18) +279*a(n-19) +497*a(n-20) -83*a(n-21) +177*a(n-22) -192*a(n-23) +50*a(n-24) -96*a(n-25) -12*a(n-26) +12*a(n-27) +12*a(n-28) for n>31

A231393 Number of (n+1)X(5+1) 0..2 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

78, 363, 1706, 8340, 41237, 217846, 1158551, 6261166, 34110556, 186830745, 1027023009, 5657597268, 31213417616, 172357775732, 952325314496, 5263831652451, 29102221456013, 160923210164607, 889929539183295

Offset: 1

R. H. Hardin, Nov 08 2013

nonn

Column 5 of A231396

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

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

A231394 Number of (n+1) X (6+1) 0..2 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

189, 1163, 7844, 55788, 401240, 3002376, 22654165, 172363558, 1318257485, 10111612656, 77748229719, 598602257116, 4613729527840, 35583008148173, 274559205933826, 2119156145505749, 16359927764473751, 126317242134114600

Offset: 1

R. H. Hardin, Nov 08 2013

nonn

Column 6 of A231396.

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

R. H. Hardin, Table of n, a(n) for n = 1..162

Cf. A231396.

A231395 Number of (n+1)X(7+1) 0..2 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

482, 3985, 35696, 345022, 3407422, 35510853, 374180527, 3979476204, 42551946612, 456361450996, 4904416040667, 52763178941654, 568116088801934, 6119806345298278, 65944807220690640, 710739805127043812

Offset: 1

R. H. Hardin, Nov 08 2013

nonn

Column 7 of A231396

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

R. H. Hardin, Table of n, a(n) for n = 1..29

A231397 Number of (1+1) X (n+1) 0..2 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

3, 7, 14, 33, 78, 189, 482, 1225, 3238, 8565, 23114, 62657, 171342, 470573, 1297330, 3586745, 9934454, 27559269, 76525210, 212662577, 591289630, 1644693789, 4576035586, 12734509097, 35443628358, 98659578197, 274645954794

Offset: 1

R. H. Hardin, Nov 08 2013

nonn

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

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

Row 1 of A231396.

Empirical: a(n) = 4*a(n-1) + a(n-2) - 16*a(n-3) + 4*a(n-4) + 24*a(n-5) - 16*a(n-6).

Empirical g.f.: x*(3 - 5*x - 17*x^2 + 18*x^3 + 32*x^4 - 32*x^5) / ((1 - x)*(1 - 2*x)*(1 - x - 6*x^2 + 8*x^4)). - Colin Barker, Sep 28 2018

A231398 Number of (2+1)X(n+1) 0..2 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

4, 8, 38, 90, 363, 1163, 3985, 14650, 50088, 185178, 665415, 2425915, 8953631, 32773916, 121530364, 449147910, 1665804417, 6189859849, 22993326811, 85585457988, 318520365520, 1186296435208, 4419902305187, 16469639460901

Offset: 1

R. H. Hardin, Nov 08 2013

nonn

Row 2 of A231396

			Some solutions for n=6
..0..0..1..0..0..1..1....0..1..1..1..1..1..2....0..1..0..0..0..0..1
..0..1..0..1..1..0..0....0..0..1..1..1..2..2....1..0..1..1..0..1..0
..1..0..1..1..0..0..0....0..0..1..1..1..2..2....0..1..1..1..1..0..1

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

Empirical: a(n) = 4*a(n-1) +12*a(n-2) -43*a(n-3) -103*a(n-4) +278*a(n-5) +418*a(n-6) -1103*a(n-7) -883*a(n-8) +2549*a(n-9) +1514*a(n-10) -4171*a(n-11) -1969*a(n-12) +4818*a(n-13) +1876*a(n-14) -3992*a(n-15) -1124*a(n-16) +2288*a(n-17) +288*a(n-18) -752*a(n-19) +96*a(n-21)

A231399 Number of (3+1)X(n+1) 0..2 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

7, 15, 100, 311, 1706, 7844, 35696, 184692, 873979, 4399412, 22162876, 110261498, 564140421, 2850848402, 14542997263, 74409026027, 380043653506, 1950717998012, 10003505335070, 51373261673575, 264098740804503, 1357567141208027

Offset: 1

R. H. Hardin, Nov 08 2013

nonn

Row 3 of A231396

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 83

Empirical recurrence of order 83 (see link above)

A231400 Number of (4+1)X(n+1) 0..2 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

12, 20, 272, 1096, 8340, 55788, 345022, 2502891, 16525492, 113585134, 799820476, 5455236715, 38507382540, 268963425191, 1882384615623, 13300278749856, 93433472155344, 659971112697126, 4663864398488500, 32941704521261841

Offset: 1

R. H. Hardin, Nov 08 2013

nonn

Row 4 of A231396

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

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

cp's OEIS Frontend

A231390 Number of (n+1) X (2+1) 0..2 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

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A231391 Number of (n+1) X (3+1) 0..2 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

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A231392 Number of (n+1)X(4+1) 0..2 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

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A231393 Number of (n+1)X(5+1) 0..2 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

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A231394 Number of (n+1) X (6+1) 0..2 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

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A231395 Number of (n+1)X(7+1) 0..2 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

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A231397 Number of (1+1) X (n+1) 0..2 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

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A231398 Number of (2+1)X(n+1) 0..2 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

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A231399 Number of (3+1)X(n+1) 0..2 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

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A231400 Number of (4+1)X(n+1) 0..2 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

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