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%I #4 Dec 16 2014 15:26:42
%S 864,1126,1048,1675,1031,1303,2670,1370,1168,1763,4349,1992,1677,1516,
%T 2587,7138,3171,2287,2151,2350,3681,12027,5056,3902,3032,3669,3476,
%U 5496,20001,7625,6103,5230,5117,5416,4905,8599,33175,12412,8650,8130,9368
%N T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and diagonal sum equal to 0 1 3 6 or 7 and every 3X3 column and antidiagonal sum not equal to 0 1 3 6 or 7
%C Table starts
%C ...864..1126..1675..2670..4349...7138..12027..20001...33175...56339....94176
%C ..1048..1031..1370..1992..3171...5056...7625..12412...19904...30526....49974
%C ..1303..1168..1677..2287..3902...6103...8650..14935...23660...33855....58675
%C ..1763..1516..2151..3032..5230...8130..11639..20350...31954...45815....80430
%C ..2587..2350..3669..5117..9368..15444..22521..43870...72344..109721...229454
%C ..3681..3476..5416..7489.14515..24076..34279..70643..120328..173799...386803
%C ..5496..4905..7492.10626.20910..33862..48579.104334..172130..244167...588270
%C ..8599..8198.13386.18971.42082..71636.109845.323902..561288..964169..3701102
%C .12992.12725.20379.28579.66739.117612.172039.548179.1058568.1616919..6650739
%C .19992.18474.28688.41037.98782.167798.240515.861326.1546722.2208135.10925806
%H R. H. Hardin, <a href="/A252305/b252305.txt">Table of n, a(n) for n = 1..312</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 60] for n>72
%F k=2: a(n) = 11*a(n-3) -42*a(n-6) +64*a(n-9) -32*a(n-12) for n>24
%F k=3: a(n) = 7*a(n-3) -14*a(n-6) +8*a(n-9) for n>18
%F k=4: a(n) = 7*a(n-3) -14*a(n-6) +8*a(n-9) for n>18
%F k=5: a(n) = 15*a(n-3) -70*a(n-6) +120*a(n-9) -64*a(n-12) for n>21
%F k=6: a(n) = 15*a(n-3) -70*a(n-6) +120*a(n-9) -64*a(n-12) for n>21
%F k=7: a(n) = 15*a(n-3) -70*a(n-6) +120*a(n-9) -64*a(n-12) for n>24
%F Empirical for row n:
%F n=2: a(n) = 11*a(n-3) -42*a(n-6) +64*a(n-9) -32*a(n-12) for n>21
%F n=3: a(n) = 7*a(n-3) -14*a(n-6) +8*a(n-9) for n>15
%F n=4: a(n) = 7*a(n-3) -14*a(n-6) +8*a(n-9) for n>15
%F n=5: a(n) = 15*a(n-3) -70*a(n-6) +120*a(n-9) -64*a(n-12) for n>21
%F n=6: a(n) = 15*a(n-3) -70*a(n-6) +120*a(n-9) -64*a(n-12) for n>21
%F n=7: a(n) = 15*a(n-3) -70*a(n-6) +120*a(n-9) -64*a(n-12) for n>19
%e Some solutions for n=4 k=4
%e ..3..0..3..0..0..0....0..0..3..3..0..3....3..0..0..3..0..0....2..0..1..2..0..1
%e ..2..1..3..2..1..3....2..1..0..2..1..0....0..1..2..0..1..2....3..3..0..3..3..0
%e ..0..1..2..3..1..2....0..1..2..0..1..2....1..3..2..1..3..2....0..2..1..0..2..1
%e ..0..0..0..0..0..3....3..0..3..3..0..3....3..0..0..3..0..0....2..0..1..2..3..1
%e ..2..1..3..2..1..0....2..1..0..2..1..3....0..1..2..0..1..0....3..3..0..0..0..3
%e ..3..1..2..0..1..2....0..1..2..0..1..2....1..3..2..1..3..2....0..2..1..3..2..1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 16 2014
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