A202889 -id:A202889 - cp's OEIS frontend

A202882 Number of n X 1 0..2 arrays with every nonzero element less than or equal to some horizontal or vertical neighbor.

1, 3, 9, 22, 51, 121, 292, 704, 1691, 4059, 9749, 23422, 56268, 135166, 324692, 779977, 1873673, 4500958, 10812237, 25973244, 62393157, 149881402, 360046432, 864906711, 2077686532, 4991036946, 11989513056, 28801314179, 69186771332

Offset: 1

R. H. Hardin, Dec 25 2011

nonn

			Some solutions for n=5
..2....2....1....0....2....2....0....1....0....1....1....0....2....1....0....2
..2....2....1....1....2....2....2....1....2....2....1....0....2....2....1....2
..0....1....1....2....0....2....2....0....2....2....1....1....1....2....1....0
..0....1....1....2....1....1....2....0....0....0....2....1....2....2....2....2
..0....0....1....2....1....1....1....0....0....0....2....1....2....0....2....2

R. H. Hardin, Table of n, a(n) for n = 1..210
T. Mansour and M. Shattuck, Counting Peaks and Valleys in a Partition of a Set, J. Int. Seq. 13 (2010), 10.6.8, Lemma 2.1, k=3, one peak.

Column 1 of A202889.

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

Empirical: G.f.: -x*(1+3*x^2+x^4)/(-1+3*x-3*x^2+4*x^3-x^4+x^5). - R. J. Mathar, Jul 09 2017

A202883 Number of n X 2 0..2 arrays with every nonzero element less than or equal to some horizontal or vertical neighbor.

Original entry on oeis.org

3, 35, 265, 1849, 13345, 96941, 701275, 5071167, 36689027, 265439091, 1920308033, 13892446697, 100505282121, 727107537885, 5260271847715, 38055531396239, 275313438949691, 1991760080088995, 14409424470217081, 104245243244589977

Offset: 1

R. H. Hardin, Dec 25 2011

nonn

Column 2 of A202889.

			Some solutions for n=5:
  2 0   2 1   2 0   0 0   0 0   0 1   2 2   2 1   1 2   2 2
  2 0   2 1   2 2   1 1   0 2   2 2   2 1   2 2   1 2   1 1
  0 2   2 1   2 2   1 0   0 2   0 1   0 0   2 0   1 2   2 1
  0 2   2 0   0 0   2 1   2 2   1 1   2 0   0 1   2 2   2 0
  0 1   1 0   1 1   2 1   2 1   2 2   2 1   1 1   0 1   1 0

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

Cf. A202889.

Empirical: a(n) = 6*a(n-1) +2*a(n-2) +46*a(n-3) +25*a(n-4) +36*a(n-5).

Empirical g.f.: (3 + 17*x + 49*x^2 + 51*x^3 + 36*x^4) / (1 - 6*x - 2*x^2 - 46*x^3 - 25*x^4 - 36*x^5). - Colin Barker, Jun 02 2018

A202884 Number of nX3 0..2 arrays with every nonzero element less than or equal to some horizontal or vertical neighbor.

Original entry on oeis.org

9, 265, 5493, 109119, 2223723, 45332961, 922352267, 18770352883, 382034229103, 7775324294349, 158245814846079, 3220677883878199, 65548442623908105, 1334066131775449299, 27151407675046583355, 552595506856781602893

Offset: 1

R. H. Hardin, Dec 25 2011

nonn

			Some solutions for n=3
..1..1..1....1..2..2....0..0..2....0..2..2....2..1..1....1..0..0....0..0..2
..1..0..2....1..2..1....0..1..2....0..1..1....2..1..0....2..2..2....2..2..2
..1..2..2....0..2..0....0..2..2....2..2..1....1..1..0....2..1..1....0..2..2

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

Column 3 of A202889.

Empirical: a(n) = 22*a(n-1) -73*a(n-2) +857*a(n-3) -1769*a(n-4) +12671*a(n-5) +21249*a(n-6) +11663*a(n-7) -43772*a(n-8) -233931*a(n-9) -841906*a(n-10) -520038*a(n-11) -711742*a(n-12) +722084*a(n-13) +4070420*a(n-14) +788112*a(n-15) -3390432*a(n-16) -1162224*a(n-17) +645120*a(n-18) +248832*a(n-19)

A202885 Number of nX4 0..2 arrays with every nonzero element less than or equal to some horizontal or vertical neighbor.

Original entry on oeis.org

22, 1849, 109119, 6092872, 348151747, 19914296913, 1137589582096, 64992189188797, 3713325091122745, 212156302986486914, 12121270553957772787, 692534079965581463725, 39567093279061401381682, 2260617527909089482464661

Offset: 1

R. H. Hardin, Dec 25 2011

nonn

			Some solutions for n=2
..0..2..2..0....2..0..2..2....0..0..1..1....2..2..0..0....1..2..1..1
..0..0..1..0....2..1..1..1....0..0..1..1....1..1..1..0....0..2..0..1

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

Column 4 of A202889.

Empirical: a(n) = 58*a(n-1) -409*a(n-2) +19812*a(n-3) -7455*a(n-4) +2592909*a(n-5) +12335100*a(n-6) -16921246*a(n-7) -80782159*a(n-8) -4256903692*a(n-9) -15824503819*a(n-10) +51444732070*a(n-11) +665973079452*a(n-12) +1722193958142*a(n-13) -9381699323187*a(n-14) -52231180624458*a(n-15) -96373950069860*a(n-16) +536481249758489*a(n-17) +2646445223858022*a(n-18) -2670449971660545*a(n-19) -23685322388362288*a(n-20) +5273037676253028*a(n-21) +123562120872374900*a(n-22) +14554488540108224*a(n-23) -423772107328693168*a(n-24) -137361850647059616*a(n-25) +951983290636001856*a(n-26) +456183082446901248*a(n-27) -1309658113153668096*a(n-28) -798409204703133696*a(n-29) +997927647389908992*a(n-30) +720498553714114560*a(n-31) -407490029986775040*a(n-32) -334751276287918080*a(n-33) +70526354545704960*a(n-34) +67405719388815360*a(n-35)

A202886 Number of nX5 0..2 arrays with every nonzero element less than or equal to some horizontal or vertical neighbor.

Original entry on oeis.org

51, 13345, 2223723, 348151747, 56006562037, 9024909392725, 1452080571954205, 233641209300452607, 37595413242729744773, 6049464276674659581373, 973416350404566342317495, 156632059367518718442398187

Offset: 1

R. H. Hardin, Dec 25 2011

nonn

			Some solutions for n=2
..2..2..1..2..2....1..0..0..2..2....1..2..2..1..0....1..1..1..2..0
..1..1..1..0..2....2..2..0..0..1....0..1..2..0..0....0..2..2..2..1

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

Column 5 of A202889.

A202887 Number of nX6 0..2 arrays with every nonzero element less than or equal to some horizontal or vertical neighbor.

Original entry on oeis.org

121, 96941, 45332961, 19914296913, 9024909392725, 4095290003129296, 1855037301620277541, 840314045399310110892, 380686256792369384392819, 172460622525800448862240139, 78128840457226148615810468318

Offset: 1

R. H. Hardin, Dec 25 2011

nonn

			Some solutions for n=2
..1..2..2..0..2..2....1..0..1..1..2..2....1..2..1..1..2..2....1..1..1..0..0..0
..0..0..1..0..1..2....1..1..0..0..0..1....0..2..2..0..0..2....0..2..2..0..2..2

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

Column 6 of A202889.

A202888 Number of nX7 0..2 arrays with every nonzero element less than or equal to some horizontal or vertical neighbor.

Original entry on oeis.org

292, 701275, 922352267, 1137589582096, 1452080571954205, 1855037301620277541, 2365289879500027706428, 3016217753359820252116493, 3846628606342304091797101743, 4905606162973199116333144693744

Offset: 1

R. H. Hardin, Dec 25 2011

nonn

			Some solutions for n=2
..0..0..0..1..1..0..2....0..1..1..2..1..1..0....0..0..2..2..0..2..2
..0..1..1..0..1..2..2....0..0..0..2..0..1..0....0..1..2..2..0..1..2

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

Column 7 of A202889.

A202881 Number of n X n 0..2 arrays with every nonzero element less than or equal to some horizontal or vertical neighbor.

Original entry on oeis.org

1, 35, 5493, 6092872, 56006562037, 4095290003129296, 2365289879500027706428, 10827985400073310953152590562, 392915439811314078675718437985175633, 112991429416970014192131075985467073204579858

Offset: 1

R. H. Hardin, Dec 25 2011

			Some solutions for n=3
..1..2..2....0..1..1....0..2..1....2..1..2....2..2..0....2..2..1....0..1..0
..1..1..1....0..2..0....1..2..2....2..2..2....2..2..1....2..1..0....1..2..0
..0..1..0....1..2..2....1..1..0....2..2..1....0..0..1....0..1..1....1..2..1

Diagonal of A202889.

cp's OEIS Frontend

A202882 Number of n X 1 0..2 arrays with every nonzero element less than or equal to some horizontal or vertical neighbor.

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A202883 Number of n X 2 0..2 arrays with every nonzero element less than or equal to some horizontal or vertical neighbor.

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A202884 Number of nX3 0..2 arrays with every nonzero element less than or equal to some horizontal or vertical neighbor.

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A202885 Number of nX4 0..2 arrays with every nonzero element less than or equal to some horizontal or vertical neighbor.

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A202886 Number of nX5 0..2 arrays with every nonzero element less than or equal to some horizontal or vertical neighbor.

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A202887 Number of nX6 0..2 arrays with every nonzero element less than or equal to some horizontal or vertical neighbor.

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A202888 Number of nX7 0..2 arrays with every nonzero element less than or equal to some horizontal or vertical neighbor.

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A202881 Number of n X n 0..2 arrays with every nonzero element less than or equal to some horizontal or vertical neighbor.

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