A252260 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 2 3 6 or 7 and every 3X3 diagonal and antidiagonal sum equal to 0 2 3 6 or 7

1072, 1331, 1331, 965, 1016, 965, 972, 562, 562, 972, 1086, 512, 596, 512, 1086, 1187, 570, 778, 778, 570, 1187, 1468, 782, 1260, 1316, 1260, 782, 1468, 1936, 1178, 1636, 1958, 1958, 1636, 1178, 1936, 2388, 1670, 2478, 2660, 3530, 2660, 2478, 1670, 2388

Offset

1,1

Comments

Table starts

.1072.1331..965...972..1086...1187...1468....1936....2388....3052.....4008

.1331.1016..562...512...570....782...1178....1670....2474....3890.....5642

..965..562..596...778..1260...1636...2478....3940....5958....9178....14534

..972..512..778..1316..1958...2660...4490....7250...10634...17954....28994

.1086..570.1260..1958..3530...6072..11762...21346...39202...80834...147842

.1187..782.1636..2660..6072...9836..17774...38612...70970..132530...284490

.1468.1178.2478..4490.11762..17774..33218...84866..142178..265730...678914

.1936.1670.3940..7250.21346..38612..84866..252162..478370.1145858..3467266

.2388.2474.5958.10634.39202..70970.142178..478370.1017410.2120450..6956290

.3052.3890.9178.17954.80834.132530.265730.1145858.2120450.4251650.18333698

Links

R. H. Hardin, Table of n, a(n) for n = 1..544

Formula

Empirical for column k:

k=1: a(n) = 5*a(n-3) +a(n-5) -8*a(n-6) -4*a(n-8) +4*a(n-9) +5*a(n-11) -2*a(n-14) for n>27

k=2: a(n) = a(n-1) +6*a(n-3) -6*a(n-4) -8*a(n-6) +8*a(n-7) for n>12

k=3: a(n) = a(n-1) +6*a(n-3) -6*a(n-4) -8*a(n-6) +8*a(n-7) for n>12

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

k=5: a(n) = a(n-1) +12*a(n-3) -12*a(n-4) -32*a(n-6) +32*a(n-7) for n>12

k=6: a(n) = a(n-1) +12*a(n-3) -12*a(n-4) -32*a(n-6) +32*a(n-7) for n>12

k=7: a(n) = a(n-1) +8*a(n-3) -8*a(n-4) for n>9

Example

Some solutions for n=4 k=4
..1..1..3..1..1..3....2..1..2..2..1..2....2..2..0..2..2..1....3..0..2..3..3..2
..3..0..1..0..0..1....3..2..3..3..2..3....3..3..2..3..3..2....2..2..0..2..2..1
..0..0..1..0..0..1....3..2..3..3..2..3....3..3..2..3..3..2....3..3..2..3..3..2
..1..1..3..1..1..2....2..1..2..2..0..2....2..2..0..2..2..0....3..3..2..3..3..2
..0..0..1..0..0..1....3..2..3..3..2..3....3..3..2..3..3..2....2..2..1..2..2..0
..0..0..1..0..3..2....3..2..3..3..2..3....0..3..2..3..0..2....3..3..2..3..3..2

Crossrefs

Column 4 is A251890 for n>2

Column 5 is A251891 for n>2

Column 6 is A251892 for n>2

Column 7 is A251893 for n>2

Sequence in context: A345525 A345779 A252257 * A085337 A085338 A250636

Adjacent sequences: A252257 A252258 A252259 * A252261 A252262 A252263

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 16 2014

Status

approved