A258891 - OEIS

%I #8 Dec 23 2018 07:26:30

%S 30870,23409,12804,9604,12544,16384,21320,27556,35360,44944,56680,

%T 70756,87680,107584,131144,158404,190240,226576,268520,315844,369920,

%U 430336,498760,574564,659744,753424,857960,972196,1098880,1236544,1388360

%N Number of (n+2) X (5+2) 0..1 arrays with no 3 x 3 subblock diagonal sum less than the antidiagonal sum or central row sum less than the central column sum.

%H R. H. Hardin, <a href="/A258891/b258891.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + 2*a(n-2) - 6*a(n-3) + 6*a(n-5) - 2*a(n-6) - 2*a(n-7) + a(n-8) for n>11.

%F Empirical for n mod 2 = 0: a(n) = n^4 + 10*n^3 + 149*n^2 + 620*n + 3844 for n>3.

%F Empirical for n mod 2 = 1: a(n) = n^4 + 10*n^3 + 150*n^2 + 610*n + 3869 for n>3.

%F Empirical g.f.: x*(30870 - 38331*x - 95754*x^2 + 122398*x^3 + 108182*x^4 - 136308*x^5 - 57626*x^6 + 59146*x^7 + 19844*x^8 - 6825*x^9 - 5404*x^10) / ((1 - x)^5*(1 + x)^3). - _Colin Barker_, Dec 23 2018

%e Some solutions for n=4:

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

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

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

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

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

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

%Y Column 5 of A258894.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jun 14 2015