A227385 -id:A227385 - cp's OEIS frontend

A227381 Number of n X n 0,1 arrays indicating 2X2 subblocks of some larger (n+1)X(n+1) binary array having a sum of one, with rows and columns of the latter in lexicographically nondecreasing order.

2, 7, 54, 1104, 61127, 8988949, 3657501287

Offset: 1

R. H. Hardin Jul 09 2013

nonn

Diagonal of A227385

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

A227382 Number of n X 3 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 4 binary array having a sum of one, with rows and columns of the latter in lexicographically nondecreasing order.

Original entry on oeis.org

4, 15, 54, 185, 587, 1704, 4532, 11126, 25430, 54568, 110768, 214130, 396492, 706695, 1217599, 2035257, 3310713, 5254953, 8157605, 12410055, 18533721, 27214306, 39342934, 56065160, 78838936, 109502710, 150354934, 204246360, 274686610

Offset: 1

R. H. Hardin, Jul 09 2013

nonn

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

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

Column 3 of A227385.

Empirical: a(n) = (1/90720)*n^9 + (1/5760)*n^8 + (1/864)*n^7 + (1/64)*n^6 - (91/864)*n^5 + (2563/1920)*n^4 - (96743/18144)*n^3 + (5083/288)*n^2 - (10643/360)*n + 31 for n>3.
Conjectures from Colin Barker, Sep 08 2018: (Start)
G.f.: x*(4 - 25*x + 84*x^2 - 160*x^3 + 207*x^4 - 179*x^5 + 107*x^6 - 42*x^7 + 19*x^9 - 16*x^10 + 6*x^11 - x^12) / (1 - x)^10.
a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>13.
(End)

A227383 Number of nX4 0,1 arrays indicating 2X2 subblocks of some larger (n+1)X5 binary array having a sum of one, with rows and columns of the latter in lexicographically nondecreasing order.

Original entry on oeis.org

5, 30, 185, 1104, 6160, 31073, 141192, 581706, 2192737, 7631150, 24723499, 75114814, 215382006, 586096131, 1520882101, 3779307010, 9026380556, 20787492011, 46293089506, 99943655427, 209652253128, 428180495383

Offset: 1

R. H. Hardin Jul 09 2013

nonn

Column 4 of A227385

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

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

Empirical: a(n) = (1/2534272925184000)*n^19 + (23/800296713216000)*n^18 + (31/29640619008000)*n^17 + (1061/31384184832000)*n^16 + (1/1793792000)*n^15 + (901/89159616000)*n^14 + (573137/7846046208000)*n^13 + (19320181/3621252096000)*n^12 - (25008281/201180672000)*n^11 + (332913253/109734912000)*n^10 - (5757514877/134120448000)*n^9 + (1008987604001/2414168064000)*n^8 - (7198243864451/3923023104000)*n^7 - (144244343741471/11769069312000)*n^6 + (12251347161947/40864824000)*n^5 - (164980284780767/59439744000)*n^4 + (28073158072/1786785)*n^3 - (35127268025713/617512896)*n^2 + (14284038375031/116396280)*n - 121172 for n>7

A227384 Number of nX5 0,1 arrays indicating 2X2 subblocks of some larger (n+1)X6 binary array having a sum of one, with rows and columns of the latter in lexicographically nondecreasing order.

Original entry on oeis.org

6, 56, 587, 6160, 61127, 550010, 4450124, 32473856, 215116595, 1303420926, 7278846827, 37731073135, 182726436203, 831526393503, 3573916903775, 14573693121509, 56609147953260, 210199678971798, 748463901892529

Offset: 1

R. H. Hardin Jul 09 2013

nonn

Column 5 of A227385

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

R. H. Hardin, Table of n, a(n) for n = 1..87
R. H. Hardin, Empirical polynomial of degree 39

Empirical polynomial of degree 39 (see link above)

cp's OEIS Frontend

A227381 Number of n X n 0,1 arrays indicating 2X2 subblocks of some larger (n+1)X(n+1) binary array having a sum of one, with rows and columns of the latter in lexicographically nondecreasing order.

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A227382 Number of n X 3 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 4 binary array having a sum of one, with rows and columns of the latter in lexicographically nondecreasing order.

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A227383 Number of nX4 0,1 arrays indicating 2X2 subblocks of some larger (n+1)X5 binary array having a sum of one, with rows and columns of the latter in lexicographically nondecreasing order.

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A227384 Number of nX5 0,1 arrays indicating 2X2 subblocks of some larger (n+1)X6 binary array having a sum of one, with rows and columns of the latter in lexicographically nondecreasing order.

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