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%I #4 Apr 16 2013 17:44:28
%S 2052,1623,1623,2471,1920,2471,3506,2493,2493,3506,4257,2863,3092,
%T 2863,4257,5737,3123,3502,3502,3123,5737,8117,4129,3775,3924,3775,
%U 4129,8117,12306,5711,4868,4209,4209,4868,5711,12306,18187,7604,6540,5371,4498
%N T(n,k)=Number of (n+3)X(k+3) 0..2 matrices with each 4X4 subblock idempotent
%C Table starts
%C ..2052..1623..2471..3506..4257..5737..8117.12306.18187.26561.38040.55162.80519
%C ..1623..1920..2493..2863..3123..4129..5711..7604..9713.12764.17344.23754.32224
%C ..2471..2493..3092..3502..3775..4868..6540..8551.10761.13991.18817.25579.34473
%C ..3506..2863..3502..3924..4209..5371..7132..9238.11551.14945.20018.27116.36445
%C ..4257..3123..3775..4209..4498..5727..7575..9778.12188.15746.21068.28510.38276
%C ..5737..4129..4868..5371..5727..7090..9090.11457.14037.17836.23484.31351.41643
%C ..8117..5711..6540..7132..7575..9090.11268.13821.16593.20653.26657.34977.45825
%C .12306..7604..8551..9238..9778.11457.13821.16568.19544.23879.30251.39038.50462
%C .18187..9713.10761.11551.12188.14037.16593.19544.22726.27344.34094.43364.55374
%C .26561.12764.13991.14945.15746.17836.20653.23879.27344.32326.39535.49373.62062
%H R. H. Hardin, <a href="/A224728/b224728.txt">Table of n, a(n) for n = 1..1681</a>
%F Empirical for column k:
%F k=1: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +a(n-4) -2*a(n-5) +2*a(n-6) -2*a(n-7) +a(n-8) for n>11
%F k=2: a(n) = 2*a(n-1) -a(n-2) +a(n-3) -2*a(n-5) +a(n-6) -2*a(n-7) +2*a(n-8) +a(n-11) -a(n-12) for n>15
%F k=3,5,7: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +4*a(n-4) -3*a(n-5) +2*a(n-7) -a(n-8) for n>10
%F k=4: a(n) = 4*a(n-1) -7*a(n-2) +8*a(n-3) -6*a(n-4) +a(n-5) +3*a(n-6) -4*a(n-7) +3*a(n-8) -a(n-9) for n>11
%F k=6: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +2*a(n-4) -5*a(n-5) +4*a(n-6) -a(n-7) -a(n-8) +2*a(n-9) -a(n-10) for n>12
%e Some solutions for n=2 k=4
%e ..1..1..1..1..1..1..0....1..0..0..0..0..0..0....1..1..1..1..0..1..0
%e ..0..0..0..0..0..0..0....1..0..0..0..0..0..0....0..0..0..0..0..0..0
%e ..0..0..0..0..0..0..0....2..0..0..0..0..0..0....0..0..0..0..0..0..0
%e ..0..0..0..0..0..0..0....2..0..0..0..0..0..0....0..0..0..0..0..0..0
%e ..0..2..1..1..1..1..1....2..0..0..0..0..0..0....2..1..1..1..1..1..1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Apr 16 2013
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