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A224665
T(n,k)=Number of n X n 0..k matrices with each 2X2 subblock idempotent
10
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Apr 14 2013
STATUS
approved