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A252114 T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and column sum equal to 0 2 3 6 or 7 and every 3X3 diagonal and antidiagonal sum not equal to 0 2 3 6 or 7 9

%I #4 Dec 14 2014 07:34:41

%S 1417,1929,1929,1568,1424,1568,1600,724,724,1600,1884,584,554,584,

%T 1884,2058,624,776,776,624,2058,2468,788,1258,1314,1258,788,2468,3149,

%U 1180,1634,1956,1956,1634,1180,3149,3950,1668,2476,2658,3528,2658,2476,1668

%N T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and column sum equal to 0 2 3 6 or 7 and every 3X3 diagonal and antidiagonal sum not equal to 0 2 3 6 or 7

%C Table starts

%C .1417.1929.1568..1600..1884...2058...2468....3149....3950....5208.....6792

%C .1929.1424..724...584...624....788...1180....1668....2472....3888.....5640

%C .1568..724..554...776..1258...1634...2476....3938....5956....9176....14532

%C .1600..584..776..1314..1956...2658...4488....7248...10632...17952....28992

%C .1884..624.1258..1956..3528...6070..11760...21344...39200...80832...147840

%C .2058..788.1634..2658..6070...9834..17772...38610...70968..132528...284488

%C .2468.1180.2476..4488.11760..17772..33216...84864..142176..265728...678912

%C .3149.1668.3938..7248.21344..38610..84864..252160..478368.1145856..3467264

%C .3950.2472.5956.10632.39200..70968.142176..478368.1017408.2120448..6956288

%C .5208.3888.9176.17952.80832.132528.265728.1145856.2120448.4251648.18333696

%H R. H. Hardin, <a href="/A252114/b252114.txt">Table of n, a(n) for n = 1..449</a>

%F Empirical for column k:

%F k=1: [linear recurrence of order 25] for n>33

%F k=2: a(n) = 6*a(n-3) -8*a(n-6) for n>13

%F k=3: a(n) = 6*a(n-3) -8*a(n-6) for n>11

%F k=4: a(n) = 4*a(n-3) for n>8

%F k=5: a(n) = 12*a(n-3) -32*a(n-6) for n>11

%F k=6: a(n) = 12*a(n-3) -32*a(n-6) for n>11

%F k=7: a(n) = 8*a(n-3) for n>8

%e Some solutions for n=4 k=4

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

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 14 2014

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Last modified May 23 18:59 EDT 2024. Contains 372765 sequences. (Running on oeis4.)