A279741 -id:A279741 - cp's OEIS frontend

A279735 Number of n X 2 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 2, 8, 26, 80, 240, 708, 2062, 5944, 16990, 48220, 136032, 381768, 1066586, 2968040, 8230370, 22751528, 62716752, 172447884, 473081830, 1295113240, 3538749862, 9652296628, 26285128896, 71472896400, 194075990450, 526312559048

Offset: 1

R. H. Hardin, Dec 18 2016

nonn

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

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

Column 2 of A279741.

Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) - a(n-4).
Conjectures from Colin Barker, Feb 11 2019: (Start)
G.f.: 2*x^2*(1 - 2*x) / (1 - 3*x + x^2)^2.
a(n) = (-1)*(2^(1-n)*(sqrt(5)*((3-sqrt(5))^n-(3+sqrt(5))^n) + 5*(3-sqrt(5))^n*(2+sqrt(5))*n - 5*(-2+sqrt(5))*(3+sqrt(5))^n*n)) / 25.
(End)

A279736 Number of n X 3 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

2, 6, 35, 168, 766, 3402, 14827, 63680, 270313, 1136546, 4740986, 19644984, 80939021, 331835984, 1354628539, 5508982340, 22328647462, 90229615030, 363633214831, 1461903606752, 5864244756909, 23476219277174, 93808204087890

Offset: 1

R. H. Hardin, Dec 18 2016

nonn

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

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

Column 3 of A279741.

Empirical: a(n) = 10*a(n-1) - 35*a(n-2) + 54*a(n-3) - 45*a(n-4) + 20*a(n-5) - 4*a(n-6) for n>7.

Empirical g.f.: x*(1 - x)*(1 - 2*x)*(2 - 8*x + 17*x^2 - 13*x^3 + 4*x^4) / (1 - 5*x + 5*x^2 - 2*x^3)^2. - Colin Barker, Feb 11 2019

A279737 Number of nX4 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

2, 14, 106, 736, 4940, 32430, 209558, 1337624, 8453760, 52990574, 329875212, 2041484910, 12570123264, 77057213940, 470543267950, 2863457284456, 17371926764454, 105101255047984, 634288745035896, 3819316295044450

Offset: 1

R. H. Hardin, Dec 18 2016

nonn

Column 4 of A279741.

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

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

Cf. A279741.

Empirical: a(n) = 20*a(n-1) -166*a(n-2) +782*a(n-3) -2465*a(n-4) +5714*a(n-5) -10213*a(n-6) +14398*a(n-7) -16186*a(n-8) +14502*a(n-9) -10252*a(n-10) +5622*a(n-11) -2332*a(n-12) +704*a(n-13) -145*a(n-14) +18*a(n-15) -a(n-16) for n>17

A279738 Number of nX5 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

5, 26, 286, 2948, 29140, 281350, 2672708, 25057618, 232453138, 2137856646, 19520180011, 177142880376, 1599086960917, 14369091541568, 128599776050102, 1146851081407532, 10195271184154052, 90377052821887506, 799110404458844621

Offset: 1

R. H. Hardin, Dec 18 2016

nonn

Column 5 of A279741.

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

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

Cf. A279741.

Empirical: a(n) = 35*a(n-1) -537*a(n-2) +4917*a(n-3) -31037*a(n-4) +147039*a(n-5) -550776*a(n-6) +1684140*a(n-7) -4287367*a(n-8) +9195097*a(n-9) -16722579*a(n-10) +25851599*a(n-11) -33949278*a(n-12) +37773854*a(n-13) -35490491*a(n-14) +28069727*a(n-15) -18639724*a(n-16) +10365480*a(n-17) -4808439*a(n-18) +1847719*a(n-19) -580867*a(n-20) +146321*a(n-21) -28520*a(n-22) +4040*a(n-23) -368*a(n-24) +16*a(n-25) for n>26

A279739 Number of nX6 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

8, 48, 746, 11434, 167904, 2407152, 33954530, 472691878, 6511502806, 88926626284, 1205703682142, 16247311565782, 217785573891544, 2905922099529922, 38618121561891188, 511391035788735602, 6750548575431539154

Offset: 1

R. H. Hardin, Dec 18 2016

nonn

Column 6 of A279741.

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 64

Cf. A279741.

Empirical recurrence of order 64 (see link above)

A279740 Number of nX7 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

15, 84, 1887, 42494, 927615, 19743140, 413326300, 8539248826, 174560480712, 3537506044402, 71169030410069, 1423001109534686, 28301960051430033, 560308589581483944, 11048008697742462541, 217065217267795946642

Offset: 1

R. H. Hardin, Dec 18 2016

nonn

Column 7 of A279741.

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

R. H. Hardin, Table of n, a(n) for n = 1..183

Cf. A279741.

A279742 Number of 2 X n 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

0, 2, 6, 14, 26, 48, 84, 146, 250, 426, 722, 1220, 2056, 3458, 5806, 9734, 16298, 27256, 45532, 75986, 126690, 211042, 351266, 584204, 970896, 1612418, 2676054, 4438526, 7357370, 12188736, 20181732, 33398930, 55244746, 91336218, 150937586

Offset: 1

R. H. Hardin, Dec 18 2016

nonn

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

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

Row 2 of A279741.

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

Empirical g.f.: 2*x^2*(1 - x^2 - 2*x^3) / ((1 - x)*(1 - x - x^2)^2). - Colin Barker, Feb 11 2019

A279743 Number of 3Xn 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

0, 8, 35, 106, 286, 746, 1887, 4700, 11553, 28104, 67759, 162144, 385583, 912098, 2147806, 5037496, 11773111, 27427532, 63715400, 147634764, 341291898, 787312776, 1812720970, 4166252110, 9559865376, 21903001872, 50112866179

Offset: 1

R. H. Hardin, Dec 18 2016

nonn

Row 3 of A279741.

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

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

Cf. A279741.

Empirical: a(n) = 6*a(n-1) -13*a(n-2) +10*a(n-3) +10*a(n-4) -30*a(n-5) +21*a(n-6) +2*a(n-7) -14*a(n-8) +10*a(n-9) -7*a(n-10) +6*a(n-11) +6*a(n-12) -2*a(n-13) -a(n-14) -2*a(n-15) -a(n-16) for n>18

A279744 Number of 4Xn 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

0, 26, 168, 736, 2948, 11434, 42494, 154886, 554894, 1962216, 6863344, 23793932, 81876322, 279975202, 952219158, 3223476464, 10867630142, 36506995228, 122242241376, 408146874402, 1359207500258, 4515810568242, 14971262615738

Offset: 1

R. H. Hardin, Dec 18 2016

nonn

Row 4 of A279741.

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

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

Cf. A279741.

Empirical: a(n) = 15*a(n-1) -97*a(n-2) +349*a(n-3) -719*a(n-4) +605*a(n-5) +988*a(n-6) -3940*a(n-7) +5528*a(n-8) -2372*a(n-9) -4242*a(n-10) +7466*a(n-11) -4480*a(n-12) +4508*a(n-13) -15704*a(n-14) +23204*a(n-15) -1380*a(n-16) -40516*a(n-17) +52888*a(n-18) -15504*a(n-19) -18615*a(n-20) -715*a(n-21) +29269*a(n-22) +10487*a(n-23) -77888*a(n-24) +64000*a(n-25) +15211*a(n-26) -48111*a(n-27) +12999*a(n-28) +903*a(n-29) +8726*a(n-30) +4570*a(n-31) -4063*a(n-32) -1491*a(n-33) -2565*a(n-34) -131*a(n-35) +130*a(n-36) +110*a(n-37) +293*a(n-38) +115*a(n-39) +104*a(n-40) +40*a(n-41) +17*a(n-42) +7*a(n-43) +a(n-44) +a(n-45) for n>50

A279745 Number of 5Xn 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

0, 80, 766, 4940, 29140, 167904, 927615, 5029822, 26842413, 141506744, 738488507, 3821661440, 19635250935, 100265767074, 509297332780, 2575109743084, 12967976929637, 65073500707556, 325507453206018, 1623623692686646

Offset: 1

R. H. Hardin, Dec 18 2016

nonn

Row 5 of A279741.

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

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

Cf. A279741.

cp's OEIS Frontend

A279735 Number of n X 2 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

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A279736 Number of n X 3 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

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A279737 Number of nX4 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

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A279738 Number of nX5 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

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A279739 Number of nX6 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

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A279740 Number of nX7 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

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A279742 Number of 2 X n 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

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A279743 Number of 3Xn 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

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A279744 Number of 4Xn 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

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A279745 Number of 5Xn 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

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