A251829 - OEIS

%I #6 Jun 02 2025 10:33:53

%S 1890,3930,3930,9354,8674,9354,22266,28202,28202,22266,61058,75498,

%T 130826,75498,61058,160322,284506,397474,397474,284506,160322,413202,

%U 1095314,2395590,1692106,2395590,1095314,413202,1139826,3073138,12830794

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

%C Table starts

%C ....1890......3930.......9354.......22266.........61058.........160322

%C ....3930......8674......28202.......75498........284506........1095314

%C ....9354.....28202.....130826......397474.......2395590.......12830794

%C ...22266.....75498.....397474.....1692106......10655426.......60427490

%C ...61058....284506....2395590....10655426.....101716526......951770218

%C ..160322...1095314...12830794....60427490.....951770218....12583469514

%C ..413202...3073138...38456182...266585018....4235688278....56477451898

%C .1139826..12215010..258040386..1720131962...41895955226...971710872170

%C .3118482..49634706.1458543158..9899825738..402976069458.13469722571314

%C .8319882.140568394.4283605290.44110390034.1784010963858.58074471696954

%H R. H. Hardin, <a href="/A251829/b251829.txt">Table of n, a(n) for n = 1..241</a>

%F Empirical for column k:

%F k=1: [linear recurrence of order 45] for n>48

%F k=2: [order 33] for n>36

%F k=3: [order 39] for n>42

%F k=4: [order 26] for n>28

%F k=5: [order 63] for n>66

%F k=6: [order 79] for n>84

%e Some solutions for n=3 k=4

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 09 2014