A279268 -id:A279268 - cp's OEIS frontend

A279262 Number of n X 2 0..1 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 4, 10, 20, 38, 68, 120, 208, 358, 612, 1042, 1768, 2992, 5052, 8514, 14324, 24062, 40364, 67624, 113160, 189150, 315844, 526890, 878160, 1462368, 2433268, 4045690, 6721748, 11160278, 18517652, 30706392, 50888128, 84287062, 139531812

Offset: 1

R. H. Hardin, Dec 08 2016

nonn

Column 2 of A279268.

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

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

Cf. A279268.

Empirical: a(n) = 3*a(n-1) - a(n-2) - 3*a(n-3) + a(n-4) + a(n-5).
Conjectures from Colin Barker, Feb 26 2018: (Start)
G.f.: 2*x^2*(1 + x)*(2 - 3*x) / ((1 - x)*(1 - x - x^2)^2).
a(n) = (1/25)*(2^(-n)*(-25*2^(2+n)+(50-6*sqrt(5))*(1-sqrt(5))^n + 50*(1+sqrt(5))^n + 6*sqrt(5)*(1+sqrt(5))^n - 5*(1-sqrt(5))^n*(1+sqrt(5))*n + 5*(-1+sqrt(5))*(1+sqrt(5))^n*n)).
(End)

A279263 Number of n X 3 0..1 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

2, 10, 29, 86, 240, 626, 1603, 4030, 9973, 24388, 59068, 141920, 338689, 803630, 1897359, 4460226, 10444904, 24376990, 56720671, 131619998, 304674313, 703690416, 1621976820, 3731637260, 8570604669, 19653441614, 45002040707

Offset: 1

R. H. Hardin, Dec 08 2016

nonn

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

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

Column 3 of A279268.

Empirical: a(n) = 4*a(n-1) - 4*a(n-2) + 2*a(n-3) - 4*a(n-4) - a(n-6) for n>9.

Empirical g.f.: x*(2 + 2*x - 3*x^2 + 6*x^3 - 8*x^5 + 5*x^6 - 4*x^7 + 2*x^8) / (1 - 2*x - x^3)^2. - Colin Barker, Feb 10 2019

A279264 Number of nX4 0..1 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

2, 20, 86, 400, 1592, 5888, 21882, 79112, 281754, 991292, 3452756, 11929580, 40936072, 139644508, 473965068, 1601601800, 5391122062, 18084715096, 60480149694, 201706042464, 671036424848, 2227380695220, 7378205313096

Offset: 1

R. H. Hardin, Dec 08 2016

nonn

Column 4 of A279268.

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

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

Cf. A279268.

Empirical: a(n) = 10*a(n-1) -37*a(n-2) +62*a(n-3) -44*a(n-4) -16*a(n-5) +109*a(n-6) -148*a(n-7) +111*a(n-8) -290*a(n-9) +399*a(n-10) -144*a(n-11) -90*a(n-12) +622*a(n-13) -605*a(n-14) +60*a(n-15) -696*a(n-16) +776*a(n-17) -6*a(n-18) -230*a(n-19) +395*a(n-20) -290*a(n-21) +80*a(n-22) +4*a(n-23) -50*a(n-24) +28*a(n-25) -16*a(n-26) +4*a(n-27) -a(n-28) for n>31

A279265 Number of nX5 0..1 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

5, 38, 240, 1592, 9042, 51568, 283450, 1526492, 8110769, 42557410, 221270081, 1141211474, 5846407067, 29780194244, 150943805823, 761780179606, 3829943970192, 19190669055102, 95869271616912, 477631625489180

Offset: 1

R. H. Hardin, Dec 08 2016

nonn

Column 5 of A279268.

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

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

Cf. A279268.

Empirical: a(n) = 18*a(n-1) -133*a(n-2) +516*a(n-3) -1014*a(n-4) +88*a(n-5) +4608*a(n-6) -8364*a(n-7) -9733*a(n-8) +59824*a(n-9) -60755*a(n-10) -158718*a(n-11) +517639*a(n-12) -285032*a(n-13) -1154479*a(n-14) +2274544*a(n-15) +553945*a(n-16) -6902900*a(n-17) +7029598*a(n-18) +7184408*a(n-19) -23703614*a(n-20) +14268016*a(n-21) +20615435*a(n-22) -34536602*a(n-23) +2729363*a(n-24) +41857034*a(n-25) -23446347*a(n-26) -35485370*a(n-27) +43282185*a(n-28) -20257546*a(n-29) -45974459*a(n-30) -10797908*a(n-31) +28946430*a(n-32) +52002920*a(n-33) +15882763*a(n-34) +101221806*a(n-35) +118400316*a(n-36) +13029146*a(n-37) -115091113*a(n-38) -148192500*a(n-39) -221179112*a(n-40) -230136184*a(n-41) -47307082*a(n-42) +115675590*a(n-43) +219033475*a(n-44) +147567712*a(n-45) +40448454*a(n-46) -16088134*a(n-47) -59742983*a(n-48) -44175096*a(n-49) -17474920*a(n-50) +609788*a(n-51) +6992661*a(n-52) +4709828*a(n-53) +2409070*a(n-54) +295024*a(n-55) -360233*a(n-56) -247676*a(n-57) -81796*a(n-58) for n>69

A279266 Number of nX6 0..1 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

8, 68, 626, 5888, 51568, 429716, 3490152, 27850092, 218952412, 1701805320, 13104577920, 100123194948, 759950374372, 5735676314072, 43078974827592, 322177736874528, 2400465164552300, 17825755365009616, 131979614009117780

Offset: 1

R. H. Hardin, Dec 08 2016

nonn

Column 6 of A279268.

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

R. H. Hardin, Table of n, a(n) for n = 1..250

Cf. A279268.

A279267 Number of nX7 0..1 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

15, 120, 1603, 21882, 283450, 3490152, 42093113, 498160278, 5812405127, 67071788240, 766923320987, 8702848263928, 98122997204330, 1100209100745782, 12277125522368779, 136425808025932376, 1510393582783303438

Offset: 1

R. H. Hardin, Dec 08 2016

nonn

Column 7 of A279268.

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

R. H. Hardin, Table of n, a(n) for n = 1..173

Cf. A279268.

cp's OEIS Frontend

A279262 Number of n X 2 0..1 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

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A279263 Number of n X 3 0..1 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

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A279264 Number of nX4 0..1 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

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A279265 Number of nX5 0..1 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

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A279266 Number of nX6 0..1 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

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A279267 Number of nX7 0..1 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

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Examples

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