A204642 T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock having three equal elements in a row horizontally, vertically, diagonally or antidiagonally exactly three ways, and new values 0..3 introduced in row major order

124, 405, 405, 1781, 1884, 1781, 4246, 5974, 5974, 4246, 16855, 379, 248, 379, 16855, 65096, 1860, 933, 933, 1860, 65096, 144255, 2239, 760, 478, 760, 2239, 144255, 651750, 8140, 2517, 1169, 1169, 2517, 8140, 651750, 2480147, 32206, 9750, 4366

Offset

1,1

Comments

Table starts

....124...405..1781..4246.16855.65096.144255.651750.2480147.6826114.28519709

....405..1884..5974...379..1860..2239...8140..32206..107738..407469..1548886

...1781..5974...248...933...760..2517...9750..28856..108520..412247..1538786

...4246...379...933...478..1169..4366...8179..29877..113861..407328..1541643

..16855..1860...760..1169..3300..3077...9482..35500..109224..410467..1557742

..65096..2239..2517..4366..3077..5446..16171..31929..113429..427632..1544127

.144255..8140..9750..8179..9482.16171..16636..40170..134630..418053..1557876

.651750.32206.28856.29877.35500.31929..40170..76664..140344..447095..1625798

Links

R. H. Hardin, Table of n, a(n) for n = 1..264

Formula

Empirical for column k:

k=1: (order 28 recurrence for n>29)

k=2: a(n) = 4*a(n-1) +a(n-2) -2*a(n-3) -19*a(n-4) -4*a(n-5) +21*a(n-6) +24*a(n-7) +3*a(n-8) -18*a(n-9) -9*a(n-10) for n>13

k=3: a(n) = 5*a(n-1) -3*a(n-2) -4*a(n-3) -12*a(n-4) +12*a(n-5) +21*a(n-6) -9*a(n-7) -9*a(n-8) for n>10

k=4: a(n) = 5*a(n-1) -3*a(n-2) -4*a(n-3) -12*a(n-4) +12*a(n-5) +21*a(n-6) -9*a(n-7) -9*a(n-8) for n>10

k=5: a(n) = 5*a(n-1) -3*a(n-2) -4*a(n-3) -12*a(n-4) +12*a(n-5) +21*a(n-6) -9*a(n-7) -9*a(n-8) for n>10

k=6: a(n) = 5*a(n-1) -3*a(n-2) -4*a(n-3) -12*a(n-4) +12*a(n-5) +21*a(n-6) -9*a(n-7) -9*a(n-8) for n>10

k=7: a(n) = 5*a(n-1) -3*a(n-2) -4*a(n-3) -12*a(n-4) +12*a(n-5) +21*a(n-6) -9*a(n-7) -9*a(n-8) for n>10

Example

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

Crossrefs

Sequence in context: A214485 A045250 A258931 * A204635 A102589 A189812

Adjacent sequences: A204639 A204640 A204641 * A204643 A204644 A204645

Keyword

nonn,tabl

Author

R. H. Hardin Jan 17 2012

Status

approved