A224665 - OEIS

%I #5 Dec 18 2015 18:18:35

%S 2,3,8,4,12,32,5,16,50,78,6,20,72,108,196,7,24,98,142,260,428,8,28,

%T 128,180,332,542,916,9,32,162,222,412,668,1126,1858,10,36,200,268,500,

%U 806,1356,2230,3678,11,40,242,318,596,956,1606,2634,4336,7096,12,44,288,372

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

%C Table starts

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

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

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

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

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

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

%C ..916.1126.1356..1606..1876..2166..2476.2806.3156.3526

%C .1858.2230.2634..3070..3538..4038..4570.5134.5730

%C .3678.4336.5046..5808..6622..7488..8406.9376

%C .7096.8246.9480.10798.12200.13686.15256

%H R. H. Hardin, <a href="/A224665/b224665.txt">Table of n, a(n) for n = 1..132</a>

%F Empirical for columns k=1..7:

%F 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

%F Empirical for row n:

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

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

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

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

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

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

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

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

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

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

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

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

%e Some solutions for n=3 k=4

%e ..1..1..4....1..0..0....1..1..3....1..0..0....1..1..1....1..1..3....1..1..2

%e ..0..0..0....1..0..0....0..0..0....1..0..0....0..0..0....0..0..0....0..0..0

%e ..3..1..1....1..0..0....0..0..0....0..0..1....1..1..1....4..1..1....2..1..1

%Y Column 1 is A224543(n-1)

%Y Row 1 is A000027(n+1)

%Y Row 2 is A008574(n+1)

%Y Row 3 is A001105(n+3)

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Apr 14 2013