A281715 -id:A281715 - cp's OEIS frontend

A281710 Number of n X 3 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

1, 7, 8, 14, 17, 22, 30, 43, 64, 98, 153, 242, 386, 619, 996, 1606, 2593, 4190, 6774, 10955, 17720, 28666, 46377, 75034, 121402, 196427, 317820, 514238, 832049, 1346278, 2178318, 3524587, 5702896, 9227474, 14930361, 24157826, 39088178

Offset: 1

R. H. Hardin, Jan 28 2017

nonn

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

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

Column 3 of A281715.

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

Empirical g.f.: x*(1 + 5*x - 6*x^2 - x^3 - 4*x^4 - 4*x^5) / ((1 - x)*(1 - x - x^2)). - Colin Barker, Feb 20 2019

A281711 Number of nX4 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

2, 14, 38, 97, 245, 631, 1625, 4234, 11017, 28652, 74521, 193836, 504195, 1311543, 3411786, 8875377, 23088294, 60062126, 156247057, 406466099, 1057396975, 2750760479, 7155964344, 18615901819, 48428431650, 125984478749, 327743372244

Offset: 1

R. H. Hardin, Jan 28 2017

nonn

Column 4 of A281715.

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

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

Cf. A281715.

Empirical: a(n) = 4*a(n-1) -2*a(n-2) -4*a(n-3) -2*a(n-4) +a(n-5) +7*a(n-6) +a(n-7) -10*a(n-8) -a(n-9) +27*a(n-10) -8*a(n-11) -18*a(n-12) +8*a(n-13) +a(n-14) -3*a(n-15) for n>16

A281712 Number of nX5 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

3, 29, 90, 294, 937, 3166, 10738, 37285, 129586, 452042, 1578499, 5515546, 19279612, 67403955, 235679364, 824104430, 2881741245, 10077105830, 35238715476, 123227200603, 430917662802, 1506893871278, 5269524537393, 18427245321410

Offset: 1

R. H. Hardin, Jan 28 2017

nonn

Column 5 of A281715.

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

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

Cf. A281715.

Empirical: a(n) = 5*a(n-1) -2*a(n-2) -9*a(n-3) -17*a(n-4) +18*a(n-5) +45*a(n-6) +5*a(n-7) -46*a(n-8) -14*a(n-9) +102*a(n-10) -101*a(n-11) +167*a(n-12) -132*a(n-13) -151*a(n-14) +2*a(n-15) -214*a(n-16) +40*a(n-17) -115*a(n-18) -55*a(n-19) -37*a(n-20) -17*a(n-21) -2*a(n-22) -15*a(n-23) +4*a(n-24) for n>28

A281713 Number of n X 6 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

5, 61, 305, 1410, 6417, 29849, 142023, 677045, 3244671, 15605137, 75182105, 362888403, 1753298751, 8477268701, 41008602681, 198445489556, 960526983294, 4649943139886, 22512991046486, 109006244562077, 527827316883602

Offset: 1

R. H. Hardin, Jan 28 2017

nonn

Column 6 of A281715.

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

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

Cf. A281715.

A281714 Number of n X 7 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

8, 126, 902, 5781, 37781, 252867, 1721319, 11737418, 80326035, 550174620, 3770023291, 25852784618, 177312917355, 1216400299609, 8345678370420, 57264137432807, 392941243651302, 2696425337315332, 18503762711566377

Offset: 1

R. H. Hardin, Jan 28 2017

nonn

Column 7 of A281715.

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

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

Cf. A281715.

A281716 Number of 2 X n 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

2, 3, 7, 14, 29, 61, 126, 265, 553, 1162, 2441, 5141, 10846, 22921, 48529, 102914, 218617, 465133, 991158, 2115193, 4520361, 9673530, 20728009, 44469637, 95515790, 205383337, 442086081, 952519602, 2054191833, 4433875101, 9578060710

Offset: 1

R. H. Hardin, Jan 28 2017

nonn

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

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

Row 2 of A281715.

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

Empirical g.f.: x*(2 - 3*x - 4*x^2 + 2*x^3 + 2*x^4) / ((1 - 2*x)*(1 - x - 3*x^2 + 2*x^4)). - Colin Barker, Feb 20 2019

A281717 Number of 3 X n 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

4, 4, 8, 38, 90, 305, 902, 2710, 8376, 25226, 77145, 235122, 715882, 2186483, 6666846, 20353268, 62140942, 189739429, 579567532, 1770391431, 5409031357, 16528102350, 50508922108, 154369025240, 471828803722, 1442250315610, 4408832591287

Offset: 1

R. H. Hardin, Jan 28 2017

nonn

Row 3 of A281715.

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

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

Cf. A281715.

Empirical: a(n) = 3*a(n-1) +8*a(n-2) -16*a(n-3) -46*a(n-4) +39*a(n-5) +121*a(n-6) -66*a(n-7) -185*a(n-8) +78*a(n-9) +216*a(n-10) -71*a(n-11) -182*a(n-12) +51*a(n-13) +107*a(n-14) -24*a(n-15) -43*a(n-16) +7*a(n-17) +10*a(n-18) -a(n-19) -a(n-20) for n>21.

A281718 Number of 4Xn 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

8, 6, 14, 97, 294, 1410, 5781, 23798, 103034, 429701, 1822286, 7734672, 32650303, 138610834, 587182558, 2488856940, 10558553240, 44771374413, 189944049261, 805892553288, 3419413103710, 14511303192013, 61585052285760

Offset: 1

R. H. Hardin, Jan 28 2017

nonn

Row 4 of A281715.

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 72

Cf. A281715.

Empirical recurrence of order 72 (see link above)

A281719 Number of 5Xn 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

16, 9, 17, 245, 937, 6417, 37781, 214045, 1321909, 7709401, 45858679, 274481652, 1621718293, 9681714758, 57586120717, 342417879408, 2040527424639, 12140992057625, 72295270999213, 430542760825365, 2563358199717255

Offset: 1

R. H. Hardin, Jan 28 2017

nonn

Row 5 of A281715.

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

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

Cf. A281715.

A281720 Number of 6Xn 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

32, 14, 22, 631, 3166, 29849, 252867, 1987696, 17241122, 141964135, 1181349593, 9947080570, 82516604643, 691237888796, 5774613619314, 48180216720264, 403021368941890, 3365534946520453, 28122510061436727, 235052865949118652

Offset: 1

R. H. Hardin, Jan 28 2017

nonn

Row 6 of A281715.

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

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

Cf. A281715.

cp's OEIS Frontend

A281710 Number of n X 3 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

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A281711 Number of nX4 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

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A281712 Number of nX5 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

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A281713 Number of n X 6 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

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A281714 Number of n X 7 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

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A281716 Number of 2 X n 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

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A281717 Number of 3 X n 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

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A281718 Number of 4Xn 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

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A281719 Number of 5Xn 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

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A281720 Number of 6Xn 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

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