A201503 -id:A201503 - cp's OEIS frontend

A201499 Number of n X n 0..1 arrays with every row and column running average nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

2, 2, 6, 8, 40, 58, 338, 526, 3334, 5448, 36168, 61108, 417920, 723354, 5054148, 8908546, 63260780, 113093022, 813360930, 1470597342, 10685501398, 19499227828, 142885700222, 262754984020, 1939096937920, 3589093760726, 26647143177214

Offset: 1

R. H. Hardin Dec 02 2011

nonn

Diagonal of A201503

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

R. H. Hardin, Table of n, a(n) for n = 1..39

A201500 Number of n X 3 0..1 arrays with every row and column running average nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

Original entry on oeis.org

2, 2, 6, 5, 12, 8, 20, 13, 30, 18, 42, 25, 56, 32, 72, 41, 90, 50, 110, 61, 132, 72, 156, 85, 182, 98, 210, 113, 240, 128, 272, 145, 306, 162, 342, 181, 380, 200, 420, 221, 462, 242, 506, 265, 552, 288, 600, 313, 650, 338, 702, 365, 756, 392, 812, 421, 870, 450, 930, 481

Offset: 1

R. H. Hardin, Dec 02 2011

nonn

Column 3 of A201503.

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

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

Cf. A201503.

Empirical: a(n) = 2*a(n-2) -2*a(n-6) +a(n-8).
Odd terms are A002378((n+1)/2).
Even terms are A000982((n+2)/2).
Empirical g.f.: x*(2 + 2*x + 2*x^2 + x^3 - 2*x^5 + x^7) / ((1 - x)^3*(1 + x)^3*(1 + x^2)). - Colin Barker, May 23 2018

A201501 Number of n X 5 0..1 arrays with every row and column running average nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

Original entry on oeis.org

2, 3, 12, 12, 40, 32, 98, 73, 204, 141, 380, 252, 650, 414, 1042, 649, 1590, 967, 2330, 1394, 3302, 1944, 4550, 2649, 6122, 3523, 8070, 4604, 10450, 5910, 13320, 7483, 16744, 9343, 20790, 11538, 25528, 14090, 31032, 17053, 37382, 20451, 44660, 24342

Offset: 1

R. H. Hardin, Dec 02 2011

nonn

Column 5 of A201503.

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

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

Cf. A201503.

Empirical: a(n) = a(n-1) +2*a(n-2) -3*a(n-3) +a(n-4) +2*a(n-5) -4*a(n-6) +2*a(n-7) +2*a(n-8) -4*a(n-9) +4*a(n-11) -2*a(n-12) -2*a(n-13) +4*a(n-14) -2*a(n-15) -a(n-16) +3*a(n-17) -2*a(n-18) -a(n-19) +a(n-20).
Even terms are A188183((n-2)/2).
Empirical g.f.: x*(2 + x + 5*x^2 + 11*x^4 - 3*x^5 + 12*x^6 + 3*x^7 + 5*x^8 - x^9 + 12*x^10 - 3*x^11 - x^12 + 5*x^13 - 2*x^14 - x^15 + 3*x^16 - 2*x^17 - x^18 + x^19) / ((1 - x)^5*(1 + x)^5*(1 - x + x^2)*(1 + x^2)^2*(1 + x^4)). - Colin Barker, May 23 2018

A201502 Number of nX7 0..1 arrays with every row and column running average nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

Original entry on oeis.org

2, 4, 20, 24, 98, 94, 338, 289, 936, 734, 2234, 1656, 4770, 3370, 9344, 6375, 17100, 11322, 29600, 19138, 48920, 30982, 77764, 48417, 119558, 73316, 178582, 108108, 260106, 155646, 370516, 219489, 517470, 303748, 710068, 413442, 959000, 554256

Offset: 1

R. H. Hardin Dec 02 2011

nonn

Column 7 of A201503

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

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

Empirical: a(n) = a(n-1) +2*a(n-2) -3*a(n-3) +a(n-4) +2*a(n-5) -4*a(n-6) +2*a(n-7) +2*a(n-8) -4*a(n-9) +a(n-10) +3*a(n-11) -3*a(n-12) +a(n-14) -a(n-15) +2*a(n-16) -a(n-17) +a(n-19) -a(n-20) +a(n-22) -a(n-23) +a(n-25) -2*a(n-26) +a(n-27) -a(n-28) +3*a(n-30) -3*a(n-31) -a(n-32) +4*a(n-33) -2*a(n-34) -2*a(n-35) +4*a(n-36) -2*a(n-37) -a(n-38) +3*a(n-39) -2*a(n-40) -a(n-41) +a(n-42)

Even terms are A188185((n-4)/2)

cp's OEIS Frontend

A201499 Number of n X n 0..1 arrays with every row and column running average nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

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A201500 Number of n X 3 0..1 arrays with every row and column running average nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

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A201501 Number of n X 5 0..1 arrays with every row and column running average nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

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A201502 Number of nX7 0..1 arrays with every row and column running average nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

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