A225011 Number of 4 X n 0..1 arrays with rows unimodal and columns nondecreasing.

5, 25, 95, 295, 791, 1897, 4166, 8518, 16414, 30086, 52834, 89402, 146446, 233108, 361711, 548591, 815083, 1188679, 1704377, 2406241, 3349193, 4601059, 6244892, 8381596, 11132876, 14644540, 19090180, 24675260, 31641640, 40272566, 50898157

Offset: 1

Author

R. H. Hardin, Apr 23 2013

Keywords

• nonn

Comments

Row 4 of A225010.

Apparently also column 5 of A071920. - R. J. Mathar, May 17 2014

Examples

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

Links

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

Crossrefs

Cf. A071920, A225010.

Formula

Empirical: a(n) = (1/40320)*n^8 + (1/1440)*n^7 + (3/320)*n^6 + (5/72)*n^5 + (629/1920)*n^4 + (1279/1440)*n^3 + (16763/10080)*n^2 + (25/24)*n + 1 = 1 + n* (n+1) *(n^6 + 27*n^5 + 351*n^4 + 2449*n^3 + 10760*n^2 + 25052*n + 42000)/40320.

Empirical: G.f.: -x*(x^4 - 5*x^3 + 10*x^2 - 10*x + 5) *(x^4 - 3*x^3 + 4*x^2 - 2*x + 1) / (x-1)^9. - R. J. Mathar, May 17 2014