A223843 Number of 7 X n 0..1 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.

8, 64, 342, 1356, 4325, 11749, 28369, 62869, 130891, 260219, 499470, 932402, 1701094, 3042926, 5348741, 9253153, 15773146, 26518532, 44008367, 72142211, 116895662, 187337832, 297106834, 466531024, 725652569, 1118500677, 1709080380, 2589696200, 3892426882, 5804817830

Offset: 1

Author

R. H. Hardin, Mar 27 2013

Keywords

• nonn

Examples

			Some solutions for n=3:
..0..0..0....1..0..0....0..0..0....0..0..0....0..0..0....0..0..1....1..0..0
..0..0..0....1..0..0....0..0..0....0..0..0....0..1..0....0..0..1....1..0..0
..0..1..0....1..1..0....1..0..0....0..0..0....0..1..0....0..0..1....1..1..0
..0..1..0....1..1..0....1..1..0....0..0..0....0..1..1....0..0..1....1..1..0
..0..1..0....1..1..0....1..1..0....1..1..0....1..1..1....0..1..1....1..1..0
..0..1..0....1..1..0....1..1..0....1..1..0....1..1..1....0..1..1....1..1..1
..0..1..0....1..1..0....1..1..1....1..1..0....1..1..1....0..1..1....1..1..1
		

Links

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

Crossrefs

Row 7 of A223838.

Formula

Empirical: a(n) = (1/87178291200)*n^14 - (1/1779148800)*n^13 + (1/45619200)*n^12 - (53/136857600)*n^11 + (137/17418240)*n^10 - (1229/29030400)*n^9 + (739771/609638400)*n^8 - (1517923/87091200)*n^7 + (321517/691200)*n^6 - (12905723/3110400)*n^5 + (4378639787/119750400)*n^4 - (369357239/2494800)*n^3 + (61973609597/151351200)*n^2 - (519380551/360360)*n + 3759 for n>8.

Extensions

Name corrected by Andrew Howroyd, Mar 18 2025