A269089 -id:A269089 - cp's OEIS frontend

A269082 Number of n X n binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two not more than once.

2, 11, 114, 2238, 80422, 5372270, 673690710, 159449028034, 71709929917104, 61507638902069052, 100988524469068110876, 318195132133780181426070, 1928131640777904103958251102, 22507425106868892327680953474828

Offset: 1

R. H. Hardin, Feb 19 2016

nonn

Diagonal of A269089.

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

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

Cf. A269089.

A269083 Number of n X 2 binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

4, 11, 30, 76, 191, 467, 1127, 2686, 6339, 14840, 34504, 79759, 183445, 420077, 958248, 2178427, 4937234, 11159252, 25160111, 56599879, 127066227, 284728994, 636922003, 1422499564, 3172350160, 7065116255, 15714769641, 34912773337

Offset: 1

R. H. Hardin, Feb 19 2016

nonn

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

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

Column 2 of A269089.

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

Empirical g.f.: x*(4 + 3*x - 4*x^2 - 9*x^3 - 5*x^4 - x^5) / (1 - x - 2*x^2 - x^3)^2. - Colin Barker, Jan 19 2019

A269084 Number of n X 3 binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

7, 30, 114, 428, 1531, 5387, 18590, 63347, 213490, 713237, 2365217, 7794642, 25549763, 83359179, 270860625, 876943006, 2830104798, 9107202178, 29230933367, 93601324315, 299085155918, 953808773503, 3036347307176, 9649992762591

Offset: 1

R. H. Hardin, Feb 19 2016

nonn

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

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

Column 3 of A269089.

Empirical: a(n) = 2*a(n-1) + 9*a(n-2) - 2*a(n-3) - 33*a(n-4) - 42*a(n-5) - 14*a(n-6) + 10*a(n-7) + 8*a(n-8) - a(n-10).

Empirical g.f.: x*(7 + 16*x - 9*x^2 - 56*x^3 - 60*x^4 - 15*x^5 + 13*x^6 + 8*x^7 - x^8 - x^9) / ((1 + x)^2*(1 - 2*x - 3*x^2 - x^3 + x^4)^2). - Colin Barker, Jan 19 2019

A269085 Number of nX4 binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

13, 76, 428, 2238, 11314, 55620, 268289, 1274435, 5982734, 27813229, 128268964, 587560638, 2675945006, 12126527636, 54715085702, 245932380152, 1101667424213, 4920048498594, 21913218006880, 97358802936939, 431593734805059

Offset: 1

R. H. Hardin, Feb 19 2016

nonn

Column 4 of A269089.

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

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

Cf. A269089.

Empirical: a(n) = 2*a(n-1) +19*a(n-2) +10*a(n-3) -122*a(n-4) -320*a(n-5) -295*a(n-6) +8*a(n-7) +176*a(n-8) +20*a(n-9) -98*a(n-10) -6*a(n-11) +43*a(n-12) -6*a(n-13) -11*a(n-14) +6*a(n-15) -a(n-16)

A269086 Number of nX5 binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

23, 191, 1531, 11314, 80422, 555789, 3761534, 25063389, 164926651, 1074440360, 6941695514, 44537043804, 284052377508, 1802408061740, 11386034886784, 71645923776799, 449267054051740, 2808501899850347, 17508131088788801

Offset: 1

R. H. Hardin, Feb 19 2016

nonn

Column 5 of A269089.

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

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

Cf. A269089.

Empirical: a(n) = 2*a(n-1) +41*a(n-2) +54*a(n-3) -509*a(n-4) -2182*a(n-5) -2830*a(n-6) +1766*a(n-7) +7914*a(n-8) +2584*a(n-9) -10583*a(n-10) -6092*a(n-11) +11506*a(n-12) +5348*a(n-13) -11688*a(n-14) -620*a(n-15) +9251*a(n-16) -4462*a(n-17) -3137*a(n-18) +4774*a(n-19) -2365*a(n-20) +338*a(n-21) +198*a(n-22) -106*a(n-23) +12*a(n-24) +4*a(n-25) -a(n-26)

A269087 Number of nX6 binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

41, 467, 5387, 55620, 555789, 5372270, 50865307, 473602013, 4353444165, 39602482120, 357186481377, 3198535920085, 28468239800885, 252053488597419, 2221493915335639, 19501164969933904, 170584538930223039

Offset: 1

R. H. Hardin, Feb 19 2016

nonn

Column 6 of A269089.

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

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

Cf. A269089.

Empirical: a(n) = 2*a(n-1) +83*a(n-2) +210*a(n-3) -1918*a(n-4) -13444*a(n-5) -27431*a(n-6) +22868*a(n-7) +172414*a(n-8) +91292*a(n-9) -572846*a(n-10) -576908*a(n-11) +1569339*a(n-12) +1662464*a(n-13) -4129647*a(n-14) -2739590*a(n-15) +10005684*a(n-16) +128072*a(n-17) -18820309*a(n-18) +14239344*a(n-19) +18275195*a(n-20) -39512592*a(n-21) +16595129*a(n-22) +32600294*a(n-23) -63035320*a(n-24) +55225574*a(n-25) -27556538*a(n-26) +5959238*a(n-27) +1367780*a(n-28) -935764*a(n-29) -205936*a(n-30) +253428*a(n-31) -6946*a(n-32) -44268*a(n-33) +5192*a(n-34) +6896*a(n-35) -1085*a(n-36) -848*a(n-37) +74*a(n-38) +94*a(n-39) +3*a(n-40) -6*a(n-41) -a(n-42)

A269088 Number of nX7 binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

72, 1127, 18590, 268289, 3761534, 50865307, 673690710, 8768989835, 112658396453, 1431998499913, 18044145807959, 225714076389625, 2806025783464923, 34698719581599414, 427098528675334433, 5235801241750340793

Offset: 1

R. H. Hardin, Feb 19 2016

nonn

Column 7 of A269089.

			Some solutions for n=3
..0..0..0..0..1..0..0. .1..0..0..0..0..1..0. .0..1..0..1..0..0..0
..0..0..0..0..0..1..1. .0..0..0..0..0..0..0. .0..0..1..0..1..0..0
..0..0..0..0..0..0..0. .1..0..0..0..1..0..0. .0..0..0..0..0..1..0

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 68

Cf. A269089.

Empirical recurrence of order 68 (see link above)

cp's OEIS Frontend

A269082 Number of n X n binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two not more than once.

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A269083 Number of n X 2 binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two not more than once.

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A269084 Number of n X 3 binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two not more than once.

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A269085 Number of nX4 binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two not more than once.

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A269086 Number of nX5 binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two not more than once.

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A269087 Number of nX6 binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two not more than once.

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A269088 Number of nX7 binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two not more than once.

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