A224665 T(n,k)=Number of n X n 0..k matrices with each 2X2 subblock idempotent.

2, 3, 8, 4, 12, 32, 5, 16, 50, 78, 6, 20, 72, 108, 196, 7, 24, 98, 142, 260, 428, 8, 28, 128, 180, 332, 542, 916, 9, 32, 162, 222, 412, 668, 1126, 1858, 10, 36, 200, 268, 500, 806, 1356, 2230, 3678, 11, 40, 242, 318, 596, 956, 1606, 2634, 4336, 7096, 12, 44, 288, 372

Offset: 1

Author

R. H. Hardin Apr 14 2013

Keywords

• nonn
• tabl

Comments

Table starts

....2....3....4.....5.....6.....7.....8....9...10...11...12...13..14..15.16.17

....8...12...16....20....24....28....32...36...40...44...48...52..56..60.64

...32...50...72....98...128...162...200..242..288..338..392..450.512.578

...78..108..142...180...222...268...318..372..430..492..558..628.702

..196..260..332...412...500...596...700..812..932.1060.1196.1340

..428..542..668...806...956..1118..1292.1478.1676.1886.2108

..916.1126.1356..1606..1876..2166..2476.2806.3156.3526

.1858.2230.2634..3070..3538..4038..4570.5134.5730

.3678.4336.5046..5808..6622..7488..8406.9376

.7096.8246.9480.10798.12200.13686.15256

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..132

Crossrefs

Column 1 is A224543(n-1)

Row 1 is A000027(n+1)

Row 2 is A008574(n+1)

Row 3 is A001105(n+3)

Formula

Empirical for columns k=1..7:

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

Empirical for row n:

n=1: a(n) = 0*n^2 + 1*n + 1

n=2: a(n) = 0*n^2 + 4*n + 4

n=3: a(n) = 2*n^2 + 12*n + 18

n=4: a(n) = 2*n^2 + 24*n + 52

n=5: a(n) = 4*n^2 + 52*n + 140

n=6: a(n) = 6*n^2 + 96*n + 326

n=7: a(n) = 10*n^2 + 180*n + 726

n=8: a(n) = 16*n^2 + 324*n + 1518

n=9: a(n) = 26*n^2 + 580*n + 3072

n=10: a(n) = 42*n^2 + 1024*n + 6030

n=11: a(n) = 68*n^2 + 1796*n + 11594

n=12: a(n) = 110*n^2 + 3128*n + 21912