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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 (list; table; graph; refs; listen; history; text; internal format)
 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 R. H. Hardin, Table of n, a(n) for n = 1..1057 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 Adjacent sequences:  A252716 A252717 A252718 * A252720 A252721 A252722 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Dec 20 2014 STATUS approved

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Last modified May 16 17:22 EDT 2021. Contains 343949 sequences. (Running on oeis4.)