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Number of (n+2)X(2+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 #4 Jun 16 2015 10:25:43

%S 2444,6271,21073,59549,130296,263417,459014,746902,1157855,1747626,

%T 2526699,3525095,4828668,6585115,8782352,11515630,14947529,19367769,

%U 24856946,31586776,39913937,50417363,63364419,79232160,98809224

%N Number of (n+2)X(2+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 2 of A259006

%H R. H. Hardin, <a href="/A259000/b259000.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = -3*a(n-1) -4*a(n-2) +a(n-3) +16*a(n-4) +33*a(n-5) +32*a(n-6) -11*a(n-7) -91*a(n-8) -156*a(n-9) -127*a(n-10) +41*a(n-11) +286*a(n-12) +443*a(n-13) +334*a(n-14) -73*a(n-15) -585*a(n-16) -860*a(n-17) -634*a(n-18) +54*a(n-19) +833*a(n-20) +1203*a(n-21) +888*a(n-22) +37*a(n-23) -845*a(n-24) -1230*a(n-25) -915*a(n-26) -135*a(n-27) +611*a(n-28) +912*a(n-29) +679*a(n-30) +153*a(n-31) -310*a(n-32) -477*a(n-33) -348*a(n-34) -93*a(n-35) +107*a(n-36) +166*a(n-37) +114*a(n-38) +30*a(n-39) -24*a(n-40) -34*a(n-41) -20*a(n-42) -4*a(n-43) +3*a(n-44) +3*a(n-45) +a(n-46) for n>60

%e Some solutions for n=4

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

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

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

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

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

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

%Y Cf. A259006

%K nonn

%O 1,1

%A _R. H. Hardin_, Jun 16 2015