A253393 - OEIS

A253393

Number of (n+1) X (4+1) 0..1 arrays with every 2 X 2 subblock antidiagonal maximum minus diagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal minimum nondecreasing vertically.

%I #7 Dec 11 2018 14:26:34

%S 180,197,246,346,465,632,823,1071,1351,1695,2079,2535,3039,3623,4263,

%T 4991,5783,6671,7631,8695,9839,11095,12439,13903,15463,17151,18943,

%U 20871,22911,25095,27399,29855,32439,35183,38063,41111,44303,47671,51191,54895

%N Number of (n+1) X (4+1) 0..1 arrays with every 2 X 2 subblock antidiagonal maximum minus diagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal minimum nondecreasing vertically.

%H R. H. Hardin, <a href="/A253393/b253393.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 3*a(n-4) - a(n-5) for n>11.

%F Empirical for n mod 2 = 0: a(n) = (2/3)*n^3 + 7*n^2 + (70/3)*n + 95 for n>6.

%F Empirical for n mod 2 = 1: a(n) = (2/3)*n^3 + 7*n^2 + (70/3)*n + 88 for n>6.

%F Empirical g.f.: x*(180 - 343*x + 15*x^2 + 362*x^3 - 227*x^4 + 10*x^5 + 8*x^6 + 4*x^7 - x^8 - x^9 + x^10) / ((1 - x)^4*(1 + x)). - _Colin Barker_, Dec 11 2018

%e Some solutions for n=4:

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

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

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

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

%Y Column 4 of A253397.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 31 2014