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T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and column sum 3 or 6 and every diagonal and antidiagonal sum not 3 or 6
9

%I #4 Dec 08 2014 10:17:29

%S 470,1142,1142,2402,4182,2402,4790,12242,12242,4790,12302,34934,43778,

%T 34934,12302,27242,132886,144818,144818,132886,27242,55766,430730,

%U 748002,524774,748002,430730,55766,148022,1317638,2861058,3849230,3849230

%N T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and column sum 3 or 6 and every diagonal and antidiagonal sum not 3 or 6

%C Table starts

%C ....470.....1142......2402.......4790........12302.........27242..........55766

%C ...1142.....4182.....12242......34934.......132886........430730........1317638

%C ...2402....12242.....43778.....144818.......748002.......2861058........9758786

%C ...4790....34934....144818.....524774......3849230......16580426.......60326174

%C ..12302...132886....748002....3849230.....39849294.....247384810.....1341002006

%C ..27242...430730...2861058...16580426....247384810....1752287522....10300749962

%C ..55766..1317638...9758786...60326174...1341002006...10300749962....63113882510

%C .148022..5134774..51133714..447979046..13904412166..154175434186..1412118575318

%C .332738.17297338.198564354.1931849642..89606678130.1105860243970.10829849843426

%C .688646.54845894.686684594.7044376358.502599987230.6575712526154.66416445639470

%H R. H. Hardin, <a href="/A251779/b251779.txt">Table of n, a(n) for n = 1..420</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1) +16*a(n-3) -16*a(n-4) -39*a(n-6) +39*a(n-7) -36*a(n-9) +36*a(n-10)

%F k=2: [order 31]

%F k=3: [order 31]

%F k=4: [order 22]

%F k=5: [order 85]

%F k=6: [order 85]

%F k=7: [order 64]

%e Some solutions for n=3 k=4

%e ..2..3..1..2..0..1....3..3..0..3..0..0....2..1..0..2..1..0....0..3..0..3..0..0

%e ..3..3..0..3..3..0....2..1..3..2..1..3....0..0..3..0..0..3....2..1..3..2..1..0

%e ..1..0..2..1..0..2....1..2..0..1..2..0....1..2..0..1..2..3....1..2..0..1..2..3

%e ..2..3..1..2..3..1....0..3..3..0..3..3....2..1..3..2..1..0....3..0..3..0..3..0

%e ..0..0..3..3..0..0....2..1..3..2..1..0....3..0..3..3..0..3....2..1..3..2..1..0

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 08 2014