A253755 - OEIS

%I #6 Jan 11 2015 11:08:35

%S 315576,3598487,17980643,54890203,112645903,199063466,333213583,

%T 513292307,740160984,1027818060,1385679480,1806669395,2293619090,

%U 2872717479,3557550957,4334258426,5205864704,6210349284,7365404092

%N 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

%C Row 7 of A253749

%H R. H. Hardin, <a href="/A253755/b253755.txt">Table of n, a(n) for n = 1..152</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>30

%F 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

%F 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

%F 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

%F 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

%e Some.solutions.for.n=1

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

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

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

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 11 2015