A202549 -id:A202549 - cp's OEIS frontend

A202545 Number of n X 4 nonnegative integer arrays each row and column an ascent sequence (interior element no greater than one plus up-steps preceding it).

1, 8, 86, 1094, 15184, 219934, 3249298, 48427802, 724492208, 10855670258, 162764756218, 2441054713126, 36613379378704, 549186530733206, 8237716581278546, 123565284853121186, 1853476648287687712

Offset: 1

R. H. Hardin, Dec 20 2011

nonn

Column 4 of A202549.

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

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

Cf. A202549.

Empirical: a(n) = 36*a(n-1) -492*a(n-2) +3418*a(n-3) -13215*a(n-4) +28650*a(n-5) -32500*a(n-6) +15000*a(n-7).

Empirical g.f.: x*(1 - 28*x + 290*x^2 - 1484*x^3 + 3983*x^4 - 5320*x^5 + 2700*x^6) / ((1 - 2*x)^3*(1 - 5*x)^3*(1 - 15*x)). - Colin Barker, Jun 01 2018

A202546 Number of nX5 nonnegative integer arrays each row and column an ascent sequence (interior element no greater than one plus up-steps preceding it).

Original entry on oeis.org

1, 16, 422, 15184, 658492, 31670778, 1605067272, 83391232150, 4381848547778, 231395948507974, 12245606508739280, 648623284638627434, 34368743751642250540, 1821371899756234451072, 96529219722687416879248

Offset: 1

R. H. Hardin Dec 20 2011

nonn

Column 5 of A202549

			Some solutions for n=4
..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
..0..1..1..1..1....0..1..0..0..1....0..0..0..1..1....0..1..0..0..0
..0..0..1..1..1....0..1..0..0..1....0..0..1..0..0....0..0..0..0..1
..0..0..1..2..0....0..1..1..1..0....0..1..0..2..0....0..0..0..1..2

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

Empirical: a(n) = 248*a(n-1) -28257*a(n-2) +1983086*a(n-3) -96716548*a(n-4) +3501247008*a(n-5) -98041897636*a(n-6) +2183731061720*a(n-7) -39467231788974*a(n-8) +587360100631792*a(n-9) -7277885948132030*a(n-10) +75715899880267428*a(n-11) -665596188648277796*a(n-12) +4967331341358415264*a(n-13) -31576803108288506292*a(n-14) +171339297288381207736*a(n-15) -794338390900258760921*a(n-16) +3145914141416297017368*a(n-17) -10629653385646120229545*a(n-18) +30565276610513057112350*a(n-19) -74504175841117536306000*a(n-20) +153099418629948633800000*a(n-21) -263226315416901561100000*a(n-22) +374833070285871009000000*a(n-23) -436066606759556920000000*a(n-24) +406749933955032200000000*a(n-25) -296248613227822500000000*a(n-26) +161980921664235000000000*a(n-27) -62416844384400000000000*a(n-28) +15084392022000000000000*a(n-29) -1716513120000000000000*a(n-30)

A202547 Number of nX6 nonnegative integer arrays each row and column an ascent sequence (interior element no greater than one plus up-steps preceding it).

Original entry on oeis.org

1, 32, 2094, 219934, 31670778, 5534917394, 1078490778110, 222425177005132, 47166084815234578, 10132160238913275232, 2189244152545815718298, 474218997901396743953114, 102831073878890605814623386

Offset: 1

R. H. Hardin Dec 20 2011

nonn

Column 6 of A202549

			Some solutions for n=4
..0..0..0..0..0..0....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..1..1..1..1....0..0..1..0..0..1....0..0..1..0..0..0
..0..1..1..1..0..2....0..1..1..2..2..1....0..0..1..0..1..2....0..0..0..1..1..1
..0..1..0..0..1..1....0..0..0..1..0..0....0..0..1..0..2..0....0..0..1..0..2..0

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

A202548 Number of nX7 nonnegative integer arrays each row and column an ascent sequence (interior element no greater than one plus up-steps preceding it).

Original entry on oeis.org

1, 64, 10438, 3249298, 1605067272, 1078490778110, 876480920594230, 794166642153146254, 762568739496974188204, 753928983875460610050918, 755888883107420734464676952, 762735395600844011293201732846

Offset: 1

R. H. Hardin Dec 20 2011

nonn

Column 7 of A202549

			Some solutions for n=4
..0..0..0..0..0..0..0....0..0..0..0..0..0..0....0..0..0..0..0..0..0
..0..0..0..1..0..0..0....0..0..0..1..1..1..1....0..0..0..1..1..1..1
..0..0..0..0..0..1..0....0..0..0..0..0..1..2....0..0..0..0..1..1..1
..0..0..1..2..0..1..0....0..1..1..2..2..1..3....0..0..0..1..2..2..2

R. H. Hardin, Table of n, a(n) for n = 1..76

A202544 Number of n X n nonnegative integer arrays with each row and column an ascent sequence (interior element no greater than one plus up-steps preceding it).

Original entry on oeis.org

1, 2, 18, 1094, 658492, 5534917394, 876480920594230, 3399581643395993926522

Offset: 1

R. H. Hardin Dec 20 2011

nonn

Diagonal of A202549

			Some solutions for n=5
..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
..0..0..0..0..0....0..0..0..0..1....0..0..0..0..1....0..0..0..1..1
..0..0..1..1..1....0..1..0..1..2....0..1..0..1..0....0..0..1..1..0
..0..0..1..2..1....0..0..1..2..3....0..1..1..0..1....0..0..1..1..1
..0..1..1..1..2....0..1..2..2..2....0..0..0..1..2....0..0..0..0..1

cp's OEIS Frontend

A202545 Number of n X 4 nonnegative integer arrays each row and column an ascent sequence (interior element no greater than one plus up-steps preceding it).

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A202546 Number of nX5 nonnegative integer arrays each row and column an ascent sequence (interior element no greater than one plus up-steps preceding it).

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A202547 Number of nX6 nonnegative integer arrays each row and column an ascent sequence (interior element no greater than one plus up-steps preceding it).

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A202548 Number of nX7 nonnegative integer arrays each row and column an ascent sequence (interior element no greater than one plus up-steps preceding it).

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A202544 Number of n X n nonnegative integer arrays with each row and column an ascent sequence (interior element no greater than one plus up-steps preceding it).

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