A253755 Number of (7+1)X(n+1) 0..2 arrays with every 2X2 subblock ne-sw antidiagonal difference nondecreasing horizontally and nw+se diagonal sum nondecreasing vertically

315576, 3598487, 17980643, 54890203, 112645903, 199063466, 333213583, 513292307, 740160984, 1027818060, 1385679480, 1806669395, 2293619090, 2872717479, 3557550957, 4334258426, 5205864704, 6210349284, 7365404092

Offset

1,1

Comments

Row 7 of A253749

Links

R. H. Hardin, Table of n, a(n) for n = 1..152

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>30

Empirical for n mod 4 = 0: a(n) = (77/60)*n^6 + (172183/1536)*n^5 + (19602983/1536)*n^4 + (162387071/384)*n^3 + (1164017641/120)*n^2 - (239316739/4)*n + 100690694 for n>11

Empirical for n mod 4 = 1: a(n) = (77/60)*n^6 + (172183/1536)*n^5 + (19602983/1536)*n^4 + (324603179/768)*n^3 + (37209009587/3840)*n^2 - (93014469101/1536)*n + (52408619321/512) for n>11

Empirical for n mod 4 = 2: a(n) = (77/60)*n^6 + (172183/1536)*n^5 + (19602983/1536)*n^4 + (162320075/384)*n^3 + (290635549/30)*n^2 - (970856271/16)*n + (3304152195/32) for n>11

Empirical for n mod 4 = 3: a(n) = (77/60)*n^6 + (172183/1536)*n^5 + (19602983/1536)*n^4 + (324811223/768)*n^3 + (37239181727/3840)*n^2 - (92096833685/1536)*n + (52080994849/512) for n>11

Example

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

Crossrefs

Sequence in context: A234656 A205984 A253748 * A309238 A153749 A186623

Adjacent sequences: A253752 A253753 A253754 * A253756 A253757 A253758

Keyword

nonn

Author

R. H. Hardin, Jan 11 2015

Status

approved