A224606 - OEIS

%I #4 Apr 11 2013 17:19:31

%S 122,178,178,297,272,297,416,371,371,416,628,449,482,449,628,1045,630,

%T 571,571,630,1045,1694,894,782,666,782,894,1694,2668,1221,1086,906,

%U 906,1086,1221,2668,4265,1707,1455,1247,1202,1247,1455,1707,4265,6922,2440

%N T(n,k)=Number of (n+2)X(k+2) 0..2 matrices with each 3X3 subblock idempotent

%C Table starts

%C ..122..178..297..416..628.1045.1694.2668..4265..6922.11196.18035.29122.47134

%C ..178..272..371..449..630..894.1221.1707..2440..3476..4979..7189.10414.15114

%C ..297..371..482..571..782.1086.1455.2010..2843..4018..5720..8226.11877.17199

%C ..416..449..571..666..906.1247.1657.2280..3216..4533..6443..9258.13358.19335

%C ..628..630..782..906.1202.1609.2091.2817..3895..5397..7564.10745.15361.22074

%C .1045..894.1086.1247.1609.2092.2656.3497..4731..6434..8878.12451.17617.25112

%C .1694.1221.1455.1657.2091.2656.3308.4272..5672..7588.10325.14312.20058.28377

%C .2668.1707.2010.2280.2817.3497.4272.5398..7007..9183.12266.16728.23125.32353

%C .4265.2440.2843.3216.3895.4731.5672.7007..8876.11367.14857.19863.26990.37220

%C .6922.3476.4018.4533.5397.6434.7588.9183.11367.14232.18194.23817.31757.43086

%H R. H. Hardin, <a href="/A224606/b224606.txt">Table of n, a(n) for n = 1..1403</a>

%F Empirical for column k:

%F k=1: a(n) = 3*a(n-1) -3*a(n-2) +2*a(n-3) -a(n-4) -a(n-5) +a(n-6) for n>7

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

%F k=3..7+: a(n) = 4*a(n-1) -6*a(n-2) +5*a(n-3) -4*a(n-4) +3*a(n-5) -a(n-6) for n>8

%e Some solutions for n=3 k=4

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

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

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

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

%e ..1..2..1..1..1..1....0..0..0..0..0..0....0..0..0..0..0..1....0..0..0..0..1..1

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Apr 11 2013