A201277 -id:A201277 - cp's OEIS frontend

A201272 Number of n X 3 0..2 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

1, 1, 4, 7, 14, 21, 41, 54, 86, 120, 168, 218, 307, 377, 496, 621, 776, 937, 1177, 1380, 1676, 1984, 2344, 2716, 3221, 3665, 4260, 4875, 5570, 6285, 7201, 8026, 9074, 10152, 11344, 12566, 14071, 15449, 17136, 18865, 20748, 22673, 24977, 27112, 29656, 32256, 35056

Offset: 0

R. H. Hardin, Nov 29 2011

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

Alois P. Heinz, Table of n, a(n) for n = 0..10000 (terms n = 1..210 from R. H. Hardin)

Column 3 of A201277.

a(n) = 2*a(n-2) + 2*a(n-3) - a(n-4) - 4*a(n-5) + 2*a(n-7) - 2*a(n-9) + 4*a(n-11) + a(n-12) - 2*a(n-13) - 2*a(n-14) + a(n-16).

G.f.: 1 + x*(1 + 4*x + 5*x^2 + 4*x^3 + 7*x^5 + 7*x^6 + 2*x^7 - x^8 + x^9 + 4*x^10 + x^11 - 2*x^12 - 2*x^13 + x^15) / ((1 - x)^5*(1 + x)^3*(1 - x + x^2)*(1 + x + x^2)^3). - Colin Barker, Mar 02 2018

a(0)=1 prepended by Alois P. Heinz, Mar 18 2024

A201271 Number of n X 2 0..2 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

Original entry on oeis.org

1, 3, 5, 4, 12, 16, 9, 27, 33, 16, 48, 56, 25, 75, 85, 36, 108, 120, 49, 147, 161, 64, 192, 208, 81, 243, 261, 100, 300, 320, 121, 363, 385, 144, 432, 456, 169, 507, 533, 196, 588, 616, 225, 675, 705, 256, 768, 800, 289, 867, 901, 324, 972, 1008, 361, 1083, 1121, 400, 1200

Offset: 0

R. H. Hardin, Nov 29 2011

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

Alois P. Heinz, Table of n, a(n) for n = 0..10000 (terms n = 1..210 from R. H. Hardin)

Column 2 of A201277.

a(n) = 3*a(n-3) -3*a(n-6) +a(n-9).
Subsequences for n modulo 3 = 1,2,0:
p=(n+2)/3: a(n) = 3*p^2
q=(n+1)/3: a(n) = 3*q^2 + 2*q
r=(n+0)/3: a(n) = r^2 + 2*r + 1.
G.f.: 1+x*(3 + 5*x + 4*x^2 + 3*x^3 + x^4 - 3*x^5 + x^8) / ((1 - x)^3*(1 + x + x^2)^3). - Colin Barker, May 22 2018

a(0)=1 prepended by Alois P. Heinz, Mar 18 2024

A201273 Number of n X 4 0..2 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

Original entry on oeis.org

1, 3, 12, 14, 85, 199, 143, 740, 1274, 759, 3416, 5312, 2746, 11628, 16676, 7946, 32164, 43438, 19713, 76321, 99347, 43137, 162566, 205231, 86351, 318364, 391600, 161089, 581578, 702330, 282904, 1006014, 1195239, 473473, 1662549, 1947164, 761467, 2641053, 3058967

Offset: 0

R. H. Hardin, Nov 29 2011

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

Alois P. Heinz, Table of n, a(n) for n = 0..10000 (terms n = 1..192 from R. H. Hardin)

Column 4 of A201277.

a(n) = a(n-3) +2*a(n-6) +a(n-9) -4*a(n-12) -5*a(n-15) +4*a(n-18) +5*a(n-21) +a(n-24) -6*a(n-27) +6*a(n-33) -a(n-36) -5*a(n-39) -4*a(n-42) +5*a(n-45) +4*a(n-48) -a(n-51) -2*a(n-54) -a(n-57) +a(n-60).

a(0)=1 prepended by Alois P. Heinz, Mar 18 2024

A201274 Number of n X 5 0..2 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

Original entry on oeis.org

1, 3, 16, 21, 199, 556, 442, 2827, 5680, 3651, 19960, 35039, 19820, 96084, 151800, 78205, 354360, 525467, 255143, 1089594, 1531163, 707770, 2908481, 3937393, 1758805, 6976823, 9145189, 3964264, 15328243, 19618905, 8309214, 31406219, 39327693, 16320584, 60602426

Offset: 0

R. H. Hardin, Nov 29 2011

nonn

			Some solutions for n=6
..0..0..0..0..0....0..0..0..0..2....0..0..0..0..0....0..0..0..0..0
..0..1..1..1..1....0..0..0..1..2....0..0..0..0..0....0..1..1..1..2
..0..1..1..1..2....0..0..0..1..2....1..1..1..2..2....0..1..1..2..2
..0..1..2..2..2....1..1..1..1..2....1..1..1..2..2....0..1..1..2..2
..0..1..2..2..2....1..1..2..2..2....1..1..1..2..2....0..1..1..2..2
..0..1..2..2..2....1..1..2..2..2....1..2..2..2..2....0..1..2..2..2

Alois P. Heinz, Table of n, a(n) for n = 0..200 (terms n = 1..141 from R. H. Hardin)

Column 5 of A201277.

a(0)=1 prepended by Alois P. Heinz, Mar 18 2024

A201275 Number of n X 6 0..2 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

Original entry on oeis.org

1, 1, 9, 41, 143, 442, 1260, 3113, 7331, 15969, 32737, 63942, 120318, 216392, 377902, 640970, 1055829, 1699241, 2679576, 4132842, 6267048, 9345121, 13712218, 19841970, 28343579, 39963063, 55722233, 76873873, 104958237, 141966994, 190366323, 253040267, 333758897

Offset: 0

R. H. Hardin, Nov 29 2011

nonn

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

Alois P. Heinz, Table of n, a(n) for n = 0..200 (terms n = 1..101 from R. H. Hardin)

Column 6 of A201277.

a(0)=1 prepended by Alois P. Heinz, Mar 18 2024

A201276 Number of n X 7 0..2 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

Original entry on oeis.org

1, 3, 27, 54, 740, 2827, 3113, 27008, 71704, 59070, 408600, 894812, 621910, 3704174, 7087046, 4373879, 23558696, 41171126, 23396689, 116650532, 190010902, 101247815, 476808796, 736407602, 373431803, 1678517670, 2482516953, 1208979602, 5235742304, 7477415626

Offset: 0

R. H. Hardin, Nov 29 2011

nonn

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

Alois P. Heinz, Table of n, a(n) for n = 0..175 (terms n = 1..82 from R. H. Hardin)

Column 7 of A201277.

a(0)=1 prepended by Alois P. Heinz, Mar 18 2024

A201270 Number of n X n 0..2 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

Original entry on oeis.org

1, 3, 5, 7, 85, 556, 1260, 27008, 215577, 613916, 16442049, 152673459, 487975060, 14392411292, 144918917509, 496264541787, 15559415313705, 165127072154120, 592098075114238, 19339952787547252, 212870280758956694, 788675446037414831, 26535438036570486429, 300014957716483809886

Offset: 0

R. H. Hardin, Nov 29 2011

nonn

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

Main diagonal of A201277.

a(0)=1 prepended and a(19)-a(23) added by Alois P. Heinz, Mar 17 2024

cp's OEIS Frontend

A201272 Number of n X 3 0..2 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

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A201271 Number of n X 2 0..2 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

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A201273 Number of n X 4 0..2 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

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A201274 Number of n X 5 0..2 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

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A201275 Number of n X 6 0..2 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

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A201276 Number of n X 7 0..2 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

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A201270 Number of n X n 0..2 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

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Examples

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