A253397 -id:A253397 - cp's OEIS frontend

A253390 Number of (n+1)X(n+1) 0..1 arrays with every 2X2 subblock antidiagonal maximum minus diagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal minimum nondecreasing vertically.

16, 102, 174, 346, 666, 1318, 2726, 5396, 11392, 22634, 47926, 95464, 201644, 402272, 846688, 1690724, 3546388, 7086130, 14818262, 29621624, 61778428, 123532896, 257035176, 514085752, 1067445536, 2135305688, 4425565336, 8853923848

Offset: 1

R. H. Hardin, Dec 31 2014

nonn

Diagonal of A253397

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

R. H. Hardin, Table of n, a(n) for n = 1..69

A253391 Number of (n+1) X (2+1) 0..1 arrays with every 2 X 2 subblock antidiagonal maximum minus diagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal minimum nondecreasing vertically.

Original entry on oeis.org

44, 102, 143, 197, 250, 320, 391, 477, 564, 666, 769, 887, 1006, 1140, 1275, 1425, 1576, 1742, 1909, 2091, 2274, 2472, 2671, 2885, 3100, 3330, 3561, 3807, 4054, 4316, 4579, 4857, 5136, 5430, 5725, 6035, 6346, 6672, 6999, 7341, 7684, 8042, 8401, 8775, 9150

Offset: 1

R. H. Hardin, Dec 31 2014

nonn

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

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

Column 2 of A253397.

Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>8.
Empirical for n mod 2 = 0: a(n) = 4*n^2 + (45/2)*n + 41 for n>4.
Empirical for n mod 2 = 1: a(n) = 4*n^2 + (45/2)*n + (75/2) for n>4.
Empirical g.f.: x*(44 + 14*x - 61*x^2 - x^3 + 16*x^4 + 4*x^5 + 2*x^6 - 2*x^7) / ((1 - x)^3*(1 + x)). - Colin Barker, Dec 11 2018

A253392 Number of (n+1) X (3+1) 0..1 arrays with every 2 X 2 subblock antidiagonal maximum minus diagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal minimum nondecreasing vertically.

Original entry on oeis.org

96, 143, 174, 246, 316, 419, 520, 651, 780, 939, 1096, 1283, 1468, 1683, 1896, 2139, 2380, 2651, 2920, 3219, 3516, 3843, 4168, 4523, 4876, 5259, 5640, 6051, 6460, 6899, 7336, 7803, 8268, 8763, 9256, 9779, 10300, 10851, 11400, 11979, 12556, 13163, 13768

Offset: 1

R. H. Hardin, Dec 31 2014

nonn

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

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

Column 3 of A253397.

Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>8.
Empirical for n mod 2 = 0: a(n) = 7*n^2 + 18*n + 59 for n>4.
Empirical for n mod 2 = 1: a(n) = 7*n^2 + 18*n + 51 for n>4.
Empirical g.f.: x*(96 - 49*x - 112*x^2 + 90*x^3 + 14*x^4 - 8*x^5 - 3*x^7) / ((1 - x)^3*(1 + x)). - Colin Barker, Dec 11 2018

A253393 Number of (n+1) X (4+1) 0..1 arrays with every 2 X 2 subblock antidiagonal maximum minus diagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal minimum nondecreasing vertically.

Original entry on oeis.org

180, 197, 246, 346, 465, 632, 823, 1071, 1351, 1695, 2079, 2535, 3039, 3623, 4263, 4991, 5783, 6671, 7631, 8695, 9839, 11095, 12439, 13903, 15463, 17151, 18943, 20871, 22911, 25095, 27399, 29855, 32439, 35183, 38063, 41111, 44303, 47671, 51191, 54895

Offset: 1

R. H. Hardin, Dec 31 2014

nonn

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

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

Column 4 of A253397.

Empirical: a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 3*a(n-4) - a(n-5) for n>11.
Empirical for n mod 2 = 0: a(n) = (2/3)*n^3 + 7*n^2 + (70/3)*n + 95 for n>6.
Empirical for n mod 2 = 1: a(n) = (2/3)*n^3 + 7*n^2 + (70/3)*n + 88 for n>6.
Empirical g.f.: x*(180 - 343*x + 15*x^2 + 362*x^3 - 227*x^4 + 10*x^5 + 8*x^6 + 4*x^7 - x^8 - x^9 + x^10) / ((1 - x)^4*(1 + x)). - Colin Barker, Dec 11 2018

A253394 Number of (n+1) X (5+1) 0..1 arrays with every 2 X 2 subblock antidiagonal maximum minus diagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal minimum nondecreasing vertically.

Original entry on oeis.org

304, 250, 316, 465, 666, 932, 1269, 1693, 2201, 2814, 3527, 4360, 5309, 6394, 7611, 8980, 10497, 12182, 14031, 16064, 18277, 20690, 23299, 26124, 29161, 32430, 35927, 39672, 43661, 47914, 52427, 57220, 62289, 67654, 73311, 79280, 85557, 92162, 99091

Offset: 1

R. H. Hardin, Dec 31 2014

nonn

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

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

Column 5 of A253397.

Empirical: a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 3*a(n-4) - a(n-5) for n>13.
Empirical for n mod 2 = 0: a(n) = (4/3)*n^3 + 13*n^2 + (5/3)*n + 164 for n>8.
Empirical for n mod 2 = 1: a(n) = (4/3)*n^3 + 13*n^2 + (5/3)*n + 161 for n>8.
Empirical g.f.: x*(304 - 662*x + 174*x^2 + 625*x^3 - 509*x^4 + 50*x^5 + 37*x^6 + 3*x^7 - 9*x^8 + 5*x^9 - 2*x^10 - x^11 + x^12) / ((1 - x)^4*(1 + x)). - Colin Barker, Dec 12 2018

A253395 Number of (n+1) X (6+1) 0..1 arrays with every 2 X 2 subblock antidiagonal maximum minus diagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal minimum nondecreasing vertically.

Original entry on oeis.org

476, 320, 419, 632, 932, 1318, 1855, 2528, 3408, 4498, 5864, 7521, 9542, 11949, 14824, 18197, 22158, 26745, 32056, 38137, 45094, 52981, 61912, 71949, 83214, 95777, 109768, 125265, 142406, 161277, 182024, 204741, 229582, 256649, 286104, 318057

Offset: 1

R. H. Hardin, Dec 31 2014

nonn

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

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

Column 6 of A253397.

Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + 5*a(n-4) - 4*a(n-5) + a(n-6) for n>16.
Empirical for n mod 2 = 0: a(n) = (1/6)*n^4 + (185/6)*n^2 - 61*n + 357 for n>10.
Empirical for n mod 2 = 1: a(n) = (1/6)*n^4 + (185/6)*n^2 - 61*n + 364 for n>10.
Empirical g.f.: x*(476 - 1584*x + 1519*x^2 + 556*x^3 - 1881*x^4 + 1054*x^5 - 48*x^6 - 106*x^7 + 20*x^8 + 12*x^9 - 23*x^10 + 17*x^11 - 5*x^12 + 2*x^14 - x^15) / ((1 - x)^5*(1 + x)). - Colin Barker, Dec 12 2018

A253396 Number of (n+1)X(7+1) 0..1 arrays with every 2X2 subblock antidiagonal maximum minus diagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal minimum nondecreasing vertically.

Original entry on oeis.org

704, 391, 520, 823, 1269, 1855, 2726, 3810, 5311, 7163, 9569, 12493, 16140, 20493, 25773, 31978, 39346, 47891, 57867, 69304, 82472, 97417, 114425, 133558, 155118, 179183, 206071, 235876, 268932, 305349, 345477, 389442, 437610, 490123, 547363

Offset: 1

R. H. Hardin, Dec 31 2014

nonn

Column 7 of A253397

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

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

Empirical: a(n) = 4*a(n-1) -5*a(n-2) +5*a(n-4) -4*a(n-5) +a(n-6) for n>18
Empirical for n mod 2 = 0: a(n) = (1/3)*n^4 - (1/3)*n^3 + (337/6)*n^2 - (1423/6)*n + 914 for n>12
Empirical for n mod 2 = 1: a(n) = (1/3)*n^4 - (1/3)*n^3 + (337/6)*n^2 - (1423/6)*n + 943 for n>12

cp's OEIS Frontend

A253390 Number of (n+1)X(n+1) 0..1 arrays with every 2X2 subblock antidiagonal maximum minus diagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal minimum nondecreasing vertically.

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A253391 Number of (n+1) X (2+1) 0..1 arrays with every 2 X 2 subblock antidiagonal maximum minus diagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal minimum nondecreasing vertically.

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A253392 Number of (n+1) X (3+1) 0..1 arrays with every 2 X 2 subblock antidiagonal maximum minus diagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal minimum nondecreasing vertically.

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A253393 Number of (n+1) X (4+1) 0..1 arrays with every 2 X 2 subblock antidiagonal maximum minus diagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal minimum nondecreasing vertically.

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A253394 Number of (n+1) X (5+1) 0..1 arrays with every 2 X 2 subblock antidiagonal maximum minus diagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal minimum nondecreasing vertically.

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A253395 Number of (n+1) X (6+1) 0..1 arrays with every 2 X 2 subblock antidiagonal maximum minus diagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal minimum nondecreasing vertically.

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A253396 Number of (n+1)X(7+1) 0..1 arrays with every 2X2 subblock antidiagonal maximum minus diagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal minimum nondecreasing vertically.

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