A253753 Number of (5+1)X(n+1) 0..2 arrays with every 2X2 subblock ne-sw antidiagonal difference nondecreasing horizontally and nw+se diagonal sum nondecreasing vertically

28107, 305707, 1636717, 5195288, 10966149, 19685575, 33767784, 53908650, 79636678, 111887770, 154273666, 208551891, 273063404, 349350730, 443497974, 557840034, 689156599, 839938280, 1019433332, 1230639389, 1468352504

Offset

1,1

Comments

Row 5 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>28

Empirical for n mod 4 = 0: a(n) = (319/768)*n^6 + (357227/7680)*n^5 + (182225/64)*n^4 + (22602713/384)*n^3 + (2800411/6)*n^2 - (128547201/40)*n + 6338652 for n>9

Empirical for n mod 4 = 1: a(n) = (319/768)*n^6 + (357227/7680)*n^5 + (182225/64)*n^4 + (15060613/256)*n^3 + (357971639/768)*n^2 - (24773998217/7680)*n + (816584243/128) for n>9

Empirical for n mod 4 = 2: a(n) = (319/768)*n^6 + (357227/7680)*n^5 + (182225/64)*n^4 + (22559891/384)*n^3 + (88566155/192)*n^2 - (265291527/80)*n + (106109999/16) for n>9

Empirical for n mod 4 = 3: a(n) = (319/768)*n^6 + (357227/7680)*n^5 + (182225/64)*n^4 + (15047617/256)*n^3 + (354548051/768)*n^2 - (25372897937/7680)*n + (845522525/128) for n>9

Example

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

Crossrefs

Sequence in context: A236093 A116462 A253746 * A203832 A237246 A281577

Adjacent sequences: A253750 A253751 A253752 * A253754 A253755 A253756

Keyword

nonn

Author

R. H. Hardin, Jan 11 2015

Status

approved