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Number of (n+2)X(4+2) 0..1 arrays with every 3X3 subblock sum of the two medians of the central row and column plus the two sums of the diagonal and antidiagonal nondecreasing horizontally, vertically and ne-to-sw antidiagonally
1

%I #5 Jun 16 2015 10:30:29

%S 34698,50654,159480,225215,177118,174655,49839,44035,31798,31346,

%T 33359,29874,33443,30974,36017,28870,34352,39506,30399,36536,31808,

%U 32858,35797,32346,35933,33482,38527,31382,36866,42022,32917,39056,34330,35382,38323

%N Number of (n+2)X(4+2) 0..1 arrays with every 3X3 subblock sum of the two medians of the central row and column plus the two sums of the diagonal and antidiagonal nondecreasing horizontally, vertically and ne-to-sw antidiagonally

%C Column 4 of A259006

%H R. H. Hardin, <a href="/A259002/b259002.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) -a(n-2) +a(n-12) -2*a(n-13) +a(n-14) for n>27

%F Empirical for n mod 12 = 0: a(n) = (1/12)*n^2 + (617/3)*n + 27362 for n>13

%F Empirical for n mod 12 = 1: a(n) = (1/12)*n^2 + (617/3)*n + (122957/4) for n>13

%F Empirical for n mod 12 = 2: a(n) = (1/12)*n^2 + (617/3)*n + (84235/3) for n>13

%F Empirical for n mod 12 = 3: a(n) = (1/12)*n^2 + (617/3)*n + (131653/4) for n>13

%F Empirical for n mod 12 = 4: a(n) = (1/12)*n^2 + (617/3)*n + 25558 for n>13

%F Empirical for n mod 12 = 5: a(n) = (1/12)*n^2 + (617/3)*n + (369979/12) for n>13

%F Empirical for n mod 12 = 6: a(n) = (1/12)*n^2 + (617/3)*n + 35777 for n>13

%F Empirical for n mod 12 = 7: a(n) = (1/12)*n^2 + (617/3)*n + (105845/4) for n>13

%F Empirical for n mod 12 = 8: a(n) = (1/12)*n^2 + (617/3)*n + (97168/3) for n>13

%F Empirical for n mod 12 = 9: a(n) = (1/12)*n^2 + (617/3)*n + (109809/4) for n>13

%F Empirical for n mod 12 = 10: a(n) = (1/12)*n^2 + (617/3)*n + 28293 for n>13

%F Empirical for n mod 12 = 11: a(n) = (1/12)*n^2 + (617/3)*n + (372271/12) for n>13

%e Some solutions for n=3

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

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

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

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

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

%Y Cf. A259006

%K nonn

%O 1,1

%A _R. H. Hardin_, Jun 16 2015