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

1,1

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

Links

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

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

Example

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

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)

Sequence in context: A198369 A193731 A193975 * A098514 A161198 A195232

Adjacent sequences: A224662 A224663 A224664 * A224666 A224667 A224668

Keyword

nonn,tabl

Author

R. H. Hardin Apr 14 2013

Status

approved