A252719 - OEIS

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.

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

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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