A201501 Number of n X 5 0..1 arrays with every row and column running average nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

2, 3, 12, 12, 40, 32, 98, 73, 204, 141, 380, 252, 650, 414, 1042, 649, 1590, 967, 2330, 1394, 3302, 1944, 4550, 2649, 6122, 3523, 8070, 4604, 10450, 5910, 13320, 7483, 16744, 9343, 20790, 11538, 25528, 14090, 31032, 17053, 37382, 20451, 44660, 24342

Offset: 1

Author

R. H. Hardin, Dec 02 2011

Keywords

• nonn

Comments

Column 5 of A201503.

Examples

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

Links

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

Crossrefs

Cf. A201503.

Formula

Empirical: a(n) = a(n-1) +2*a(n-2) -3*a(n-3) +a(n-4) +2*a(n-5) -4*a(n-6) +2*a(n-7) +2*a(n-8) -4*a(n-9) +4*a(n-11) -2*a(n-12) -2*a(n-13) +4*a(n-14) -2*a(n-15) -a(n-16) +3*a(n-17) -2*a(n-18) -a(n-19) +a(n-20).

Even terms are A188183((n-2)/2).

Empirical g.f.: x*(2 + x + 5*x^2 + 11*x^4 - 3*x^5 + 12*x^6 + 3*x^7 + 5*x^8 - x^9 + 12*x^10 - 3*x^11 - x^12 + 5*x^13 - 2*x^14 - x^15 + 3*x^16 - 2*x^17 - x^18 + x^19) / ((1 - x)^5*(1 + x)^5*(1 - x + x^2)*(1 + x^2)^2*(1 + x^4)). - Colin Barker, May 23 2018