|
%I #6 Jan 19 2015 13:15:05
%S 8392,30184,124496,451721,992616,2326216,4928792,8796936,15429736,
%T 25901691,41279336,64590680,98433380,147871688,219336822,319580553,
%U 459762302,656093206,925811194,1292791666,1788288642,2455569322
%N Number of (n+2)X(3+2) 0..1 arrays with every 3X3 subblock diagonal sum plus antidiagonal sum nondecreasing horizontally and vertically
%C Column 3 of A253935
%H R. H. Hardin, <a href="/A253930/b253930.txt">Table of n, a(n) for n = 1..210</a>
%H R. H. Hardin, <a href="/A253930/a253930.txt">Empirical quasipolynomial</a>
%F Empirical: a(n) = 5*a(n-1) -12*a(n-2) +20*a(n-3) -20*a(n-4) -4*a(n-5) +54*a(n-6) -118*a(n-7) +161*a(n-8) -125*a(n-9) -8*a(n-10) +216*a(n-11) -425*a(n-12) +509*a(n-13) -398*a(n-14) +78*a(n-15) +370*a(n-16) -770*a(n-17) +972*a(n-18) -852*a(n-19) +417*a(n-20) +195*a(n-21) -804*a(n-22) +1188*a(n-23) -1230*a(n-24) +918*a(n-25) -336*a(n-26) -336*a(n-27) +918*a(n-28) -1230*a(n-29) +1188*a(n-30) -804*a(n-31) +195*a(n-32) +417*a(n-33) -852*a(n-34) +972*a(n-35) -770*a(n-36) +370*a(n-37) +78*a(n-38) -398*a(n-39) +509*a(n-40) -425*a(n-41) +216*a(n-42) -8*a(n-43) -125*a(n-44) +161*a(n-45) -118*a(n-46) +54*a(n-47) -4*a(n-48) -20*a(n-49) +20*a(n-50) -12*a(n-51) +5*a(n-52) -a(n-53) for n>83
%F Empirical polynomial of degree 13 plus a quasipolynomial of degree 8 with period 24 for n>30 (see link above)
%e Some solutions for n=3
%e ..0..0..0..1..1....0..0..0..0..0....0..0..1..1..0....0..1..0..0..1
%e ..0..0..0..0..1....0..0..0..1..0....0..0..0..1..1....0..0..0..0..1
%e ..0..1..1..1..1....0..0..0..1..0....0..1..1..1..0....0..0..1..1..1
%e ..0..1..1..1..0....0..0..0..1..1....1..1..1..1..1....1..0..0..0..0
%e ..1..0..1..1..0....1..0..1..1..1....1..1..1..0..1....0..1..1..0..1
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 19 2015
| 