A224728 T(n,k)=Number of (n+3)X(k+3) 0..2 matrices with each 4X4 subblock idempotent

2052, 1623, 1623, 2471, 1920, 2471, 3506, 2493, 2493, 3506, 4257, 2863, 3092, 2863, 4257, 5737, 3123, 3502, 3502, 3123, 5737, 8117, 4129, 3775, 3924, 3775, 4129, 8117, 12306, 5711, 4868, 4209, 4209, 4868, 5711, 12306, 18187, 7604, 6540, 5371, 4498

Offset

1,1

Comments

Table starts

..2052..1623..2471..3506..4257..5737..8117.12306.18187.26561.38040.55162.80519

..1623..1920..2493..2863..3123..4129..5711..7604..9713.12764.17344.23754.32224

..2471..2493..3092..3502..3775..4868..6540..8551.10761.13991.18817.25579.34473

..3506..2863..3502..3924..4209..5371..7132..9238.11551.14945.20018.27116.36445

..4257..3123..3775..4209..4498..5727..7575..9778.12188.15746.21068.28510.38276

..5737..4129..4868..5371..5727..7090..9090.11457.14037.17836.23484.31351.41643

..8117..5711..6540..7132..7575..9090.11268.13821.16593.20653.26657.34977.45825

.12306..7604..8551..9238..9778.11457.13821.16568.19544.23879.30251.39038.50462

.18187..9713.10761.11551.12188.14037.16593.19544.22726.27344.34094.43364.55374

.26561.12764.13991.14945.15746.17836.20653.23879.27344.32326.39535.49373.62062

Links

R. H. Hardin, Table of n, a(n) for n = 1..1681

Formula

Empirical for column k:

k=1: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +a(n-4) -2*a(n-5) +2*a(n-6) -2*a(n-7) +a(n-8) for n>11

k=2: a(n) = 2*a(n-1) -a(n-2) +a(n-3) -2*a(n-5) +a(n-6) -2*a(n-7) +2*a(n-8) +a(n-11) -a(n-12) for n>15

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

k=4: a(n) = 4*a(n-1) -7*a(n-2) +8*a(n-3) -6*a(n-4) +a(n-5) +3*a(n-6) -4*a(n-7) +3*a(n-8) -a(n-9) for n>11

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

Example

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

Crossrefs

Sequence in context: A183842 A253711 A168176 * A224721 A224720 A320277

Adjacent sequences: A224725 A224726 A224727 * A224729 A224730 A224731

Keyword

nonn,tabl

Author

R. H. Hardin Apr 16 2013

Status

approved