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

1,1

Comments

Column 5 of A204651.

Links

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

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)

Example

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

Crossrefs

Cf. A204651.

Sequence in context: A349307 A349308 A224547 * A202447 A202440 A248432

Adjacent sequences: A204645 A204646 A204647 * A204649 A204650 A204651

Keyword

nonn

Author

R. H. Hardin, Jan 17 2012

Status

approved