A253754 Number of (6+1) X (n+1) 0..2 arrays with every 2 X 2 subblock ne-sw antidiagonal difference nondecreasing horizontally and nw+se diagonal sum nondecreasing vertically.

95940, 1087364, 5648005, 17656505, 36766701, 64166071, 106040628, 163826702, 237829299, 329185796, 441266948, 578004976, 740961618, 931230442, 1153821258, 1414293119, 1714268872, 2054996968, 2443657919, 2887832232, 3389327580

Offset

1,1

Comments

Row 6 of A253749.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +4*a(n-4) -12*a(n-5) +12*a(n-6) -4*a(n-7) -6*a(n-8) +18*a(n-9) -18*a(n-10) +6*a(n-11) +4*a(n-12) -12*a(n-13) +12*a(n-14) -4*a(n-15) -a(n-16) +3*a(n-17) -3*a(n-18) +a(n-19) for n>29.

Empirical for n mod 4 = 0: a(n) = (8701/11520)*n^6 + (357037/7680)*n^5 + (47126897/9216)*n^4 + (17388329/128)*n^3 + (7788618871/2880)*n^2 - (1949149903/120)*n + 28887765 for n>10.

Empirical for n mod 4 = 1: a(n) = (8701/11520)*n^6 + (357037/7680)*n^5 + (47126897/9216)*n^4 + (17393303/128)*n^3 + (62317012313/23040)*n^2 - (124224186997/7680)*n + (29328794513/1024) for n>10.

Empirical for n mod 4 = 2: a(n) = (8701/11520)*n^6 + (357037/7680)*n^5 + (47126897/9216)*n^4 + (17390121/128)*n^3 + (15573815537/5760)*n^2 - (1951787653/120)*n + (1859970205/64) for n>10.

Empirical for n mod 4 = 3: a(n) = (8701/11520)*n^6 + (357037/7680)*n^5 + (47126897/9216)*n^4 + (17385409/128)*n^3 + (62288990453/23040)*n^2 - (125420117317/7680)*n + (30008700921/1024) for n>10.

Example

Some solutions for n=1
..1..2....0..1....0..0....0..0....0..0....0..1....0..1....0..0....1..2....1..0
..0..1....0..0....2..0....0..2....2..0....1..0....0..1....1..2....2..2....2..1
..2..2....2..0....1..0....0..2....2..0....1..0....0..1....1..1....1..1....2..0
..0..0....2..0....1..1....1..2....2..2....0..0....0..1....2..2....2..2....2..0
..1..2....0..0....0..1....1..2....2..2....1..2....1..2....1..1....2..2....2..0
..2..1....2..2....0..2....2..2....2..2....1..1....2..1....1..2....2..2....1..1
..1..0....2..1....0..2....1..1....2..2....1..1....0..1....2..2....1..2....0..2

Crossrefs

Cf. A253749.

Sequence in context: A234478 A130001 A253747 * A236779 A116228 A116253

Adjacent sequences: A253751 A253752 A253753 * A253755 A253756 A253757

Keyword

nonn

Author

R. H. Hardin, Jan 11 2015

Status

approved