A253754 - OEIS

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.

%I #8 Jun 26 2022 20:07:17

%S 95940,1087364,5648005,17656505,36766701,64166071,106040628,163826702,

%T 237829299,329185796,441266948,578004976,740961618,931230442,

%U 1153821258,1414293119,1714268872,2054996968,2443657919,2887832232,3389327580

%N 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.

%C Row 6 of A253749.

%H R. H. Hardin, <a href="/A253754/b253754.txt">Table of n, a(n) for n = 1..210</a>

%F 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.

%F 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.

%F 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.

%F 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.

%F 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.

%e Some solutions for n=1

%e ..1..2....0..1....0..0....0..0....0..0....0..1....0..1....0..0....1..2....1..0

%e ..0..1....0..0....2..0....0..2....2..0....1..0....0..1....1..2....2..2....2..1

%e ..2..2....2..0....1..0....0..2....2..0....1..0....0..1....1..1....1..1....2..0

%e ..0..0....2..0....1..1....1..2....2..2....0..0....0..1....2..2....2..2....2..0

%e ..1..2....0..0....0..1....1..2....2..2....1..2....1..2....1..1....2..2....2..0

%e ..2..1....2..2....0..2....2..2....2..2....1..1....2..1....1..2....2..2....1..1

%e ..1..0....2..1....0..2....1..1....2..2....1..1....0..1....2..2....1..2....0..2

%Y Cf. A253749.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 11 2015