A296320 -id:A296320 - cp's OEIS frontend

A296314 Number of n X n 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 1 neighboring 1.

1, 6, 32, 434, 12547, 676269, 78105580, 18043360170, 8435284786616, 8062065704707386, 15602483060688719807, 61357587200669343827967, 490367520450812937863879738, 7957358933563948031830555664333

Offset: 1

R. H. Hardin, Dec 10 2017

nonn

Diagonal of A296320.

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

R. H. Hardin, Table of n, a(n) for n = 1..16

Cf. A296320.

A296315 Number of n X 3 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 1 neighboring 1.

Original entry on oeis.org

3, 11, 32, 96, 295, 902, 2747, 8380, 25577, 78021, 238029, 726211, 2215568, 6759403, 20622067, 62915288, 191946374, 585603549, 1786600798, 5450687951, 16629344149, 50733978916, 154782809780, 472222339285, 1440689299042, 4395356771500

Offset: 1

R. H. Hardin, Dec 10 2017

nonn

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

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

Column 3 of A296320.

Empirical: a(n) = a(n-1) + 4*a(n-2) + 6*a(n-3) + 3*a(n-4) - 3*a(n-6) + a(n-7) - 3*a(n-9) + a(n-11).

Empirical g.f.: x*(3 + 8*x + 9*x^2 + 2*x^3 - 4*x^4 - 2*x^5 + 2*x^6 - 3*x^7 - 3*x^8 + x^9 + x^10) / ((1 + x^2 - x^3)*(1 - x - 5*x^2 - 4*x^3 + x^4 - x^5 - 2*x^6 + x^7 + x^8)). - Colin Barker, Feb 23 2019

A296316 Number of n X 4 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 1 neighboring 1.

Original entry on oeis.org

4, 27, 96, 434, 1970, 8470, 37431, 164807, 723019, 3180521, 13980961, 61446863, 270126432, 1187392203, 5219407184, 22943336005, 100852689192, 443321760393, 1948727874003, 8566095221354, 37654312064817, 165518509370616

Offset: 1

R. H. Hardin, Dec 10 2017

nonn

Column 4 of A296320.

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

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

Cf. A296320.

Empirical: a(n) = a(n-1) +6*a(n-2) +29*a(n-3) +30*a(n-4) +61*a(n-5) +9*a(n-6) +73*a(n-7) -93*a(n-8) +134*a(n-9) -201*a(n-10) +173*a(n-11) -179*a(n-12) +107*a(n-13) -a(n-14) -30*a(n-15) -15*a(n-16) +22*a(n-17) -3*a(n-18) -2*a(n-19) -a(n-20) +a(n-21).

A296317 Number of nX5 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 1 neighboring 1.

Original entry on oeis.org

6, 60, 295, 1970, 12547, 77426, 490668, 3078638, 19343899, 121656933, 764438509, 4805307635, 30204033317, 189843766164, 1193281179607, 7500358766425, 47143616101848, 296322172696548, 1862536668117625, 11707004939753233

Offset: 1

R. H. Hardin, Dec 10 2017

nonn

Column 5 of A296320.

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

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

Cf. A296320.

Empirical: a(n) = a(n-1) +16*a(n-2) +80*a(n-3) +121*a(n-4) +307*a(n-5) +211*a(n-6) +756*a(n-7) -1102*a(n-8) +1314*a(n-9) -6584*a(n-10) +10104*a(n-11) -18601*a(n-12) +10716*a(n-13) +10312*a(n-14) -5396*a(n-15) -7685*a(n-16) +42214*a(n-17) -18367*a(n-18) -47060*a(n-19) -19762*a(n-20) +48147*a(n-21) +841*a(n-22) +16545*a(n-23) +5633*a(n-24) -23751*a(n-25) +3993*a(n-26) -4983*a(n-27) -5719*a(n-28) +4682*a(n-29) +79*a(n-30) +1960*a(n-31) +1488*a(n-32) +26*a(n-33) -4*a(n-34) -270*a(n-35) -171*a(n-36) -96*a(n-37) -21*a(n-38) +15*a(n-39) +3*a(n-40) +8*a(n-41) +a(n-43)

A296318 Number of nX6 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 1 neighboring 1.

Original entry on oeis.org

9, 132, 902, 8470, 77426, 676269, 6069953, 54182821, 482859661, 4309680012, 38447587452, 343001529054, 3060175277029, 27301498644398, 243572477909485, 2173052663274029, 19387068214074941, 172963318405155953

Offset: 1

R. H. Hardin, Dec 10 2017

nonn

Column 6 of A296320.

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 85

Cf. A296320.

Empirical recurrence of order 85 (see link above)

A296319 Number of nX7 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 1 neighboring 1.

Original entry on oeis.org

13, 301, 2747, 37431, 490668, 6069953, 78105580, 994666167, 12644605701, 161191403242, 2052476777491, 26138049499179, 332906349627080, 4239664089907890, 53994948962929686, 687661857639787158

Offset: 1

R. H. Hardin, Dec 10 2017

nonn

Column 7 of A296320.

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

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

Cf. A296320.

cp's OEIS Frontend

A296314 Number of n X n 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 1 neighboring 1.

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A296315 Number of n X 3 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 1 neighboring 1.

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A296316 Number of n X 4 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 1 neighboring 1.

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A296317 Number of nX5 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 1 neighboring 1.

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A296318 Number of nX6 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 1 neighboring 1.

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A296319 Number of nX7 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 1 neighboring 1.

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