A252254 - OEIS

%I #4 Dec 16 2014 07:19:14

%S 318,260,260,278,239,278,352,242,242,352,463,268,231,268,463,616,302,

%T 249,249,302,616,847,359,279,267,279,359,847,1160,437,318,297,297,318,

%U 437,1160,1625,549,366,336,327,336,366,549,1625,2281,707,444,384,366,366,384

%N T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and column sum not equal to 0 3 5 6 or 7 and every 3X3 diagonal and antidiagonal sum equal to 0 3 5 6 or 7

%C Table starts

%C ..318.260.278.352.463.616.847.1160.1625.2281.3237.4631.6575.9496.13664.19579

%C ..260.239.242.268.302.359.437..549..707..919.1239.1682.2274.3182..4435..6115

%C ..278.242.231.249.279.318.366..444..546..672..876.1143.1473.2007..2706..3570

%C ..352.268.249.267.297.336.384..462..564..690..894.1161.1491.2025..2724..3588

%C ..463.302.279.297.327.366.414..492..594..720..924.1191.1521.2055..2754..3618

%C ..616.359.318.336.366.405.453..531..633..759..963.1230.1560.2094..2793..3657

%C ..847.437.366.384.414.453.501..579..681..807.1011.1278.1608.2142..2841..3705

%C .1160.549.444.462.492.531.579..657..759..885.1089.1356.1686.2220..2919..3783

%C .1625.707.546.564.594.633.681..759..861..987.1191.1458.1788.2322..3021..3885

%C .2281.919.672.690.720.759.807..885..987.1113.1317.1584.1914.2448..3147..4011

%H R. H. Hardin, <a href="/A252254/b252254.txt">Table of n, a(n) for n = 1..880</a>

%F Empirical for column k:

%F k=1: [linear recurrence of order 18] for n>25

%F k=2: [order 12] for n>16

%F k=3: a(n) = a(n-1) +3*a(n-3) -3*a(n-4) -a(n-6) +a(n-7) for n>9

%F k=4: a(n) = a(n-1) +3*a(n-3) -3*a(n-4) -a(n-6) +a(n-7) for n>9

%F k=5: a(n) = a(n-1) +3*a(n-3) -3*a(n-4) -a(n-6) +a(n-7) for n>9

%F k=6: a(n) = a(n-1) +3*a(n-3) -3*a(n-4) -a(n-6) +a(n-7) for n>9

%F k=7: a(n) = a(n-1) +3*a(n-3) -3*a(n-4) -a(n-6) +a(n-7) for n>9

%e Some solutions for n=4 k=4

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

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 16 2014