A250783 -id:A250783 - cp's OEIS frontend

A250788 Number of (6+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

288, 796, 2010, 5028, 12036, 27986, 63184, 139436, 301786, 643164, 1353544, 2820050, 5828064, 11966884, 24444622, 49725780, 100817008, 203857762, 411330612, 828530748, 1666582118, 3348596476, 6722194620, 13484879538

Offset: 1

R. H. Hardin, Nov 27 2014

nonn

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

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

Row 6 of A250783.

Empirical: a(n) = 7*a(n-1) - 18*a(n-2) + 17*a(n-3) + 8*a(n-4) - 29*a(n-5) + 18*a(n-6) + 3*a(n-7) - 7*a(n-8) + 2*a(n-9).

Empirical g.f.: 2*x*(144 - 610*x + 811*x^2 + 195*x^3 - 1408*x^4 + 1026*x^5 + 137*x^6 - 421*x^7 + 128*x^8) / ((1 - x)^5*(1 + x)*(1 - 2*x)*(1 - x - x^2)). - Colin Barker, Nov 20 2018

A250789 Number of (7+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

Original entry on oeis.org

576, 1596, 4054, 10306, 25126, 59590, 137082, 307762, 676266, 1460260, 3107536, 6535280, 13611742, 28129720, 57764876, 118015794, 240116940, 486922786, 984765176, 1987317314, 4003558184, 8054089024, 16184388422, 32492334224

Offset: 1

R. H. Hardin, Nov 27 2014

nonn

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

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

Row 7 of A250783.

Empirical: a(n) = 8*a(n-1) - 25*a(n-2) + 35*a(n-3) - 9*a(n-4) - 37*a(n-5) + 47*a(n-6) - 15*a(n-7) - 10*a(n-8) + 9*a(n-9) - 2*a(n-10).

Empirical g.f.: 2*x*(288 - 1506*x + 2843*x^2 - 1193*x^3 - 3324*x^4 + 5009*x^5 - 1866*x^6 - 1087*x^7 + 1094*x^8 - 256*x^9) / ((1 - x)^6*(1 + x)*(1 - 2*x)*(1 - x - x^2)). - Colin Barker, Nov 20 2018

A250776 Number of (n+1)X(n+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

Original entry on oeis.org

9, 46, 230, 1152, 5688, 27986, 137082, 670608, 3275574, 15987988, 77980390, 380145754, 1852275976, 9021572492, 43923360572, 213777365336

Offset: 1

R. H. Hardin, Nov 27 2014

nonn

Diagonal of A250783

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

cp's OEIS Frontend

A250788 Number of (6+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

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A250789 Number of (7+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

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A250776 Number of (n+1)X(n+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

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