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

1,1

Comments

Column 5 of A201503.

Links

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

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

Example

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

Crossrefs

Cf. A201503.

Sequence in context: A081529 A002944 A266366 * A370548 A302843 A037321

Adjacent sequences: A201498 A201499 A201500 * A201502 A201503 A201504

Keyword

nonn

Author

R. H. Hardin, Dec 02 2011

Status

approved