A204648 Number of (n+1) X 6 0..1 arrays with column and row pair sums b(i,j)=a(i,j)+a(i,j-1) and c(i,j)=a(i,j)+a(i-1,j) nondecreasing in column and row directions, respectively.

80, 137, 284, 571, 1076, 1918, 3261, 5329, 8408, 12867, 19162, 27859, 39640, 55328, 75895, 102489, 136444, 179309, 232860, 299131, 380428, 479362, 598865, 742225, 913104, 1115575, 1354142, 1633779, 1959952, 2338660, 2776459, 3280505, 3858580

Offset: 1

Author

R. H. Hardin, Jan 17 2012

Keywords

• nonn

Comments

Column 5 of A204651.

Examples

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

Links

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

Crossrefs

Cf. A204651.

Formula

Empirical: a(n) = 6*a(n-1) -14*a(n-2) +14*a(n-3) -14*a(n-5) +14*a(n-6) -6*a(n-7) +a(n-8) for n>11.

Conjectures from Colin Barker, Jun 08 2018: (Start)

G.f.: x*(80 - 343*x + 582*x^2 - 335*x^3 - 292*x^4 + 600*x^5 - 379*x^6 + 89*x^7 - 4*x^8 + 8*x^9 - 4*x^10) / ((1 - x)^7*(1 + x)).

a(n) = (-10080 + 43776*n + 15308*n^2 + 2970*n^3 + 620*n^4 + 54*n^5 + 2*n^6)/1440 for n>3 and even.

a(n) = (-10890 + 43776*n + 15308*n^2 + 2970*n^3 + 620*n^4 + 54*n^5 + 2*n^6)/1440 for n>3 and odd.

(End)