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

Author

R. H. Hardin Apr 14 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Diagonal is A224659(n+1)

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