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A252719
T(n,k) = Number of (n+2) X (k+2) 0..3 arrays with every consecutive three elements in every row and diagonal having exactly two distinct values, and in every column and antidiagonal not having exactly two distinct values, and new values 0 upwards introduced in row major order.
16
39, 52, 45, 70, 46, 54, 96, 50, 56, 84, 129, 63, 62, 76, 111, 175, 69, 70, 80, 102, 165, 237, 91, 86, 97, 119, 154, 257, 319, 107, 110, 112, 135, 170, 220, 376, 432, 131, 114, 132, 147, 178, 224, 306, 560, 584, 163, 158, 153, 191, 214, 257, 341, 478, 930, 786, 207, 194
OFFSET
1,1
COMMENTS
Table starts
..39..52..70..96.129.175.237..319..432..584..786.1067.1442.1947.2651.3593.4873
..45..46..50..63..69..91.107..131..163..207..243..319..395..479..619..783..939
..54..56..62..70..86.110.114..158..194..214..290..374..402..566..722..790.1106
..84..76..80..97.112.132.153..196..224..277..352..420..513..676..800..997.1312
.111.102.119.135.147.191.211..251..323..375..447..599..691..851.1139.1335.1647
.165.154.170.178.214.262.270..354..434..466..622..790..846.1170.1490.1618.2254
.257.220.224.257.288.324.373..452..512..617..768..900.1093.1412.1664.2057.2688
.376.306.341.368.383.478.522..586..746..846..982.1294.1482.1786.2378.2766.3382
.560.478.494.492.564.664.672..836.1012.1060.1376.1720.1824.2468.3124.3364.4640
.930.700.656.722.768.828.938.1084.1208.1422.1720.1980.2378.3004.3512.4302.5560
LINKS
FORMULA
Empirical for column k:
k=1: [linear recurrence of order 9] for n>11
k=2: a(n) = a(n-1) +7*a(n-3) -7*a(n-4) -12*a(n-6) +12*a(n-7) for n>9
k=3: a(n) = a(n-1) +3*a(n-3) -3*a(n-4) for n>6
k=4: [order 10] for n>12
k=5: [same order 10] for n>12
k=6: a(n) = a(n-1) +3*a(n-3) -3*a(n-4) -a(n-6) +a(n-7) for n>9
k=7: a(n) = 6*a(n-3) -11*a(n-6) +5*a(n-9) +2*a(n-12) -a(n-15) for n>17
Empirical for row n:
n=1: [linear recurrence of order 13] for n>14
n=2: a(n) = a(n-2) +2*a(n-3) -2*a(n-5) for n>8
n=3: a(n) = a(n-2) +2*a(n-3) -2*a(n-5) for n>6
n=4: a(n) = -a(n-1) +3*a(n-3) +3*a(n-4) -2*a(n-6) -2*a(n-7) for n>8
n=5: a(n) = -a(n-1) +3*a(n-3) +3*a(n-4) -2*a(n-6) -2*a(n-7) for n>9
n=6: a(n) = -a(n-1) +3*a(n-3) +3*a(n-4) -2*a(n-6) -2*a(n-7) for n>9
n=7: a(n) = -a(n-1) +3*a(n-3) +3*a(n-4) -2*a(n-6) -2*a(n-7) for n>9
EXAMPLE
Some solutions for n=4, k=4
..0..1..0..0..1..0....0..0..1..0..0..1....0..1..1..2..1..1....0..0..1..1..2..2
..0..0..1..0..0..1....2..1..1..2..1..1....3..1..3..3..1..3....3..3..0..0..1..1
..0..2..2..0..2..2....1..2..1..1..2..1....1..1..0..1..1..2....2..2..3..3..0..0
..0..3..0..0..1..0....0..0..1..0..0..1....2..1..1..0..1..1....1..1..2..2..3..3
..0..0..3..0..0..1....2..1..1..2..1..1....3..1..3..3..1..3....0..0..1..1..2..1
..0..2..2..0..2..2....1..2..1..1..2..1....1..1..2..1..1..0....3..3..0..0..1..0
CROSSREFS
Sequence in context: A181488 A020305 A216978 * A252720 A070145 A133676
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 20 2014
STATUS
approved