%I #8 Oct 03 2025 23:28:01

%S 452,370,370,512,340,512,739,428,428,739,990,517,514,517,990,1345,611,

%T 629,629,611,1345,1852,775,728,752,728,775,1852,2659,1044,929,861,861,

%U 929,1044,2659,3846,1383,1232,1091,974,1091,1232,1383,3846,5589,1808

%N T(n,k)=Number of (n+3)X(k+3) 0..1 matrices with each 4X4 subblock idempotent.

%C Table starts

%C ..452..370..512..739..990.1345.1852.2659.3846.5589..8064.11675.16954.24757

%C ..370..340..428..517..611..775.1044.1383.1808.2373..3190..4323..5868..7946

%C ..512..428..514..629..728..929.1232.1627.2095.2739..3658..4945..6670..9010

%C ..739..517..629..752..861.1091.1433.1871.2390.3108..4136..5571..7493.10098

%C ..990..611..728..861..974.1233.1614.2099.2665.3459..4600..6193..8316.11198

%C .1345..775..929.1091.1233.1550.1997.2558.3206.4115..5408..7202..9577.12793

%C .1852.1044.1232.1433.1614.1997.2526.3175.3917.4951..6416..8429.11076.14646

%C .2659.1383.1627.1871.2099.2558.3175.3918.4764.5935..7582..9826.12763.16709

%C .3846.1808.2095.2390.2665.3206.3917.4764.5716.7032..8871.11362.14599.18939

%C .5589.2373.2739.3108.3459.4115.4951.5935.7032.8536.10610.13395.16987.21782

%H R. H. Hardin, <a href="/A224568/b224568.txt">Table of n, a(n) for n = 1..1798</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>10

%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: 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=5: 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=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

%F k=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=8: 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=9: 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=10: 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

%F k=11: 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=12: 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

%e Some solutions for n=3 k=4

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

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Apr 10 2013