A250782 Number of (n+1) X (7+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.

901, 2326, 5568, 12796, 28692, 63184, 137082, 293588, 621664, 1303276, 2708612, 5587548, 11454008, 23356632, 47422730, 95949660, 193592124, 389742628, 783299900, 1572215204, 3152596828, 6316933760, 12650561098, 25324612868

Offset: 1

Author

R. H. Hardin, Nov 27 2014

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Column 7 of A250783.

Formula

Empirical: a(n) = 12*a(n-1) - 65*a(n-2) + 210*a(n-3) - 450*a(n-4) + 672*a(n-5) - 714*a(n-6) + 540*a(n-7) - 285*a(n-8) + 100*a(n-9) - 21*a(n-10) + 2*a(n-11).

Conjectures from Colin Barker, Nov 19 2018: (Start)

G.f.: x*(901 - 8486*x + 36221*x^2 - 92040*x^3 + 154050*x^4 - 177432*x^5 + 142536*x^6 - 79028*x^7 + 29083*x^8 - 6482*x^9 + 681*x^10) / ((1 - x)^10*(1 - 2*x)).

a(n) = (45360*(3025*2^n-2344) - 70509024*n - 9423432*n^2 - 6541100*n^3 + 254142*n^4 - 151725*n^5 + 6552*n^6 - 870*n^7 + 18*n^8 - n^9) / 90720.

(End)