%I #12 Nov 16 2015 04:45:03
%S 9374,18341,55760,116098,142316,191035,134036,138255,135282,125066,
%T 136926,137549,144388,157396,164184,173168,185086,194970,199468,
%U 222173,221824,227101,257586,254779,269678,292721,283212,305637,337320,325206
%N Number of (n+2)X(3+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 3 of A259006.
%H R. H. Hardin, <a href="/A259001/b259001.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = -a(n-1) -a(n-2) +a(n-3) +a(n-4) +2*a(n-5) +a(n-6) +a(n-7) -a(n-8) -a(n-9) -a(n-10) +a(n-12) +a(n-13) +a(n-14) -a(n-15) -a(n-16) -2*a(n-17) -a(n-18) -a(n-19) +a(n-20) +a(n-21) +a(n-22) for n>36.
%F Also empirically a quasipolynomial of degree 2 with period 60, the first 12 being (empirical formulas for n>14):
%F for n mod 60 = 0: a(n) = (307/3)*n^2 + (175303/30)*n + 53785;
%F for n mod 60 = 1: a(n) = (3107/24)*n^2 + (109097/20)*n + (6308123/120);
%F for n mod 60 = 2: a(n) = (10769/72)*n^2 + (977923/180)*n + (2138171/45);
%F for n mod 60 = 3: a(n) = (307/3)*n^2 + (175303/30)*n + (523367/10);
%F for n mod 60 = 4: a(n) = (3107/24)*n^2 + (109097/20)*n + (815764/15);
%F for n mod 60 = 5: a(n) = (10769/72)*n^2 + (977923/180)*n + (3756257/72);
%F for n mod 60 = 6: a(n) = (307/3)*n^2 + (175303/30)*n + (289877/5);
%F for n mod 60 = 7: a(n) = (3107/24)*n^2 + (109097/20)*n + (5353751/120);
%F for n mod 60 = 8: a(n) = (10769/72)*n^2 + (977923/180)*n + (2363234/45);
%F for n mod 60 = 9: a(n) = (307/3)*n^2 + (175303/30)*n + (556181/10);
%F for n mod 60 = 10: a(n) = (3107/24)*n^2 + (109097/20)*n + (141317/3);
%F for n mod 60 = 11: a(n) = (10769/72)*n^2 + (977923/180)*n + (19746049/360).
%e Some solutions for n=4:
%e ..0..0..0..1..1....0..0..0..1..1....1..1..0..0..0....0..1..0..0..1
%e ..0..0..0..0..0....0..0..1..0..1....0..0..0..1..0....1..0..0..0..1
%e ..0..0..0..0..1....0..0..0..0..1....0..0..0..0..1....1..0..1..1..1
%e ..1..1..1..1..1....1..1..1..1..0....1..1..1..1..1....1..0..0..0..0
%e ..1..0..1..1..1....0..1..1..1..0....0..1..1..1..1....1..1..1..1..0
%e ..1..0..1..1..0....0..1..1..0..1....1..1..0..0..1....0..1..0..1..1
%Y Cf. A259006.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jun 16 2015