A224676 T(n,k)=Number of (n+1)X(k+1) 0..2 matrices with each 2X2 subblock idempotent

12, 25, 25, 41, 50, 41, 70, 76, 76, 70, 115, 123, 108, 123, 115, 189, 191, 170, 170, 191, 189, 308, 300, 257, 260, 257, 300, 308, 501, 470, 398, 381, 381, 398, 470, 501, 813, 741, 617, 573, 542, 573, 617, 741, 813, 1318, 1173, 967, 864, 793, 793, 864, 967, 1173, 1318

Offset

1,1

Comments

Table starts

...12...25...41...70..115..189..308..501...813..1318..2135..3457..5596..9057

...25...50...76..123..191..300..470..741..1173..1866..2980..4775..7671.12348

...41...76..108..170..257..398..617..967..1525..2421..3862..6185..9934.15990

...70..123..170..260..381..573..864.1322..2043..3191..5026..7972.12713.20357

..115..191..257..381..542..793.1166.1746..2650..4080..6355..9996.15843.25257

..189..300..398..573..793.1126.1608.2343..3471..5236..8022.12457.19553.30950

..308..470..617..864.1166.1608.2230.3157..4554..6711.10083.15415.23907.37504

..501..741..967.1322.1746.2343.3157.4336..6072..8705.12767.19130.29198.45247

..813.1173.1525.2043.2650.3471.4554.6072..8246.11470.16359.23922.35783.54575

.1318.1866.2421.3191.4080.5236.6711.8705.11470.15458.21373.30371.44312.66212

Links

R. H. Hardin, Table of n, a(n) for n = 1..967

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1) -a(n-3)

k=2: a(n) = 4*a(n-1) -5*a(n-2) +a(n-3) +2*a(n-4) -a(n-5)

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

Example

Some solutions for n=3 k=4
..1..1..1..1..0....1..0..1..0..2....1..0..1..0..0....0..1..0..0..2
..0..0..0..0..0....1..0..1..0..1....1..0..1..0..1....0..1..0..0..1
..0..0..0..0..0....1..0..1..0..1....1..0..1..0..1....0..1..0..0..1
..0..0..1..1..1....0..0..1..0..1....1..0..1..0..1....0..1..0..0..1

Crossrefs

Diagonal is A224659(n+1)

Sequence in context: A249134 A323195 A033165 * A239147 A136739 A372029

Adjacent sequences: A224673 A224674 A224675 * A224677 A224678 A224679

Keyword

nonn,tabl

Author

R. H. Hardin Apr 14 2013

Status

approved