A227025 -id:A227025 - cp's OEIS frontend

A227021 Number of n X 2 (0,1,2) arrays of permanents of 2 X 2 subblocks of some (n+1) X 3 binary array with rows and columns of the latter in lexicographically nondecreasing order.

7, 26, 72, 171, 368, 729, 1343, 2325, 3819, 6001, 9082, 13311, 18978, 26417, 36009, 48185, 63429, 82281, 105340, 133267, 166788, 206697, 253859, 309213, 373775, 448641, 534990, 634087, 747286, 876033, 1021869, 1186433, 1371465, 1578809

Offset: 1

R. H. Hardin, Jun 27 2013

nonn

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

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

Column 2 of A227025.

Empirical: a(n) = (1/40)*n^5 + (1/3)*n^4 - (1/8)*n^3 + (5/3)*n^2 + (141/10)*n - 15 for n>2.
Conjectures from Colin Barker, Sep 06 2018: (Start)
G.f.: x*(7 - 16*x + 21*x^2 - 11*x^3 + 7*x^4 - 6*x^5 + x^7) / (1 - x)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
(End)

A227022 Number of nX3 (0,1,2) arrays of permanents of 2X2 subblocks of some (n+1)X4 binary array with rows and columns of the latter in lexicographically nondecreasing order.

Original entry on oeis.org

12, 72, 335, 1366, 4948, 16115, 47659, 129463, 326522, 771653, 1722005, 3652726, 7406710, 14426468, 27103102, 49288384, 87029344, 149600861, 250930856, 411535151, 661105246, 1041922558, 1613307461, 2457351181, 3686223670

Offset: 1

R. H. Hardin Jun 27 2013

nonn

Column 3 of A227025

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

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

Empirical: a(n) = (1/2217600)*n^11 + (1/48384)*n^10 + (19/241920)*n^9 + (199/2800)*n^7 - (4291/11520)*n^6 - (3567/1792)*n^5 + (1336261/24192)*n^4 - (95295341/302400)*n^3 + (851237/1440)*n^2 + (8658337/9240)*n - 3550 for n>6

A227023 Number of nX4 (0,1,2) arrays of permanents of 2X2 subblocks of some (n+1)X5 binary array with rows and columns of the latter in lexicographically nondecreasing order.

Original entry on oeis.org

18, 171, 1366, 10050, 65317, 375270, 1924848, 8908719, 37616613, 146387460, 529743352, 1796459014, 5746888515, 17440783714, 50456503591, 139731086307, 371756133099, 953183208702, 2361809765393, 5669196636680, 13211336518266

Offset: 1

R. H. Hardin Jun 27 2013

nonn

Column 4 of A227025

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

R. H. Hardin, Table of n, a(n) for n = 1..37

A227024 Number of nX5 (0,1,2) arrays of permanents of 2X2 subblocks of some (n+1)X6 binary array with rows and columns of the latter in lexicographically nondecreasing order.

Original entry on oeis.org

25, 368, 4948, 65317, 786154, 8379285, 79224749, 668706345, 5081503151, 35102679286, 222533536879, 1305789511714, 7145426639248, 36700964912428, 177929765359899, 818153315837912, 3583007628524884, 14999102522624015

Offset: 1

R. H. Hardin Jun 27 2013

nonn

Column 5 of A227025

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

R. H. Hardin, Table of n, a(n) for n = 1..29

A227020 Number of n X n (0,1,2) arrays of permanents of 2X2 subblocks of some (n+1)X(n+1) binary array with rows and columns of the latter in lexicographically nondecreasing order.

Original entry on oeis.org

3, 26, 335, 10050, 786154, 168973605, 104606988712

Offset: 1

R. H. Hardin Jun 27 2013

nonn

Diagonal of A227025

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

cp's OEIS Frontend

A227021 Number of n X 2 (0,1,2) arrays of permanents of 2 X 2 subblocks of some (n+1) X 3 binary array with rows and columns of the latter in lexicographically nondecreasing order.

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A227022 Number of nX3 (0,1,2) arrays of permanents of 2X2 subblocks of some (n+1)X4 binary array with rows and columns of the latter in lexicographically nondecreasing order.

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A227023 Number of nX4 (0,1,2) arrays of permanents of 2X2 subblocks of some (n+1)X5 binary array with rows and columns of the latter in lexicographically nondecreasing order.

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A227024 Number of nX5 (0,1,2) arrays of permanents of 2X2 subblocks of some (n+1)X6 binary array with rows and columns of the latter in lexicographically nondecreasing order.

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A227020 Number of n X n (0,1,2) arrays of permanents of 2X2 subblocks of some (n+1)X(n+1) binary array with rows and columns of the latter in lexicographically nondecreasing order.

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