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 A224559 T(n,k)=Number of (n+2)X(k+2) 0..1 matrices with each 3X3 subblock idempotent 9

%I

%S 50,70,70,113,94,113,172,133,133,172,263,174,180,174,263,418,246,230,

%T 230,246,418,669,351,320,286,320,351,669,1064,492,451,395,395,451,492,

%U 1064,1699,693,620,551,540,551,620,693,1699,2734,992,866,749,740,740,749,866

%N T(n,k)=Number of (n+2)X(k+2) 0..1 matrices with each 3X3 subblock idempotent

%C Table starts

%C ...50...70..113..172..263..418..669.1064.1699.2734..4409..7108.11471.18538

%C ...70...94..133..174..246..351..492..693..992.1418..2036..2937..4253..6169

%C ..113..133..180..230..320..451..620..866.1229.1746..2493..3586..5178..7498

%C ..172..174..230..286..395..551..749.1041.1473.2086..2973..4273..6166..8925

%C ..263..246..320..395..540..740..988.1351.1881.2623..3689..5243..7494.10763

%C ..418..351..451..551..740..992.1298.1742.2382.3267..4530..6362..9003.12826

%C ..669..492..620..749..988.1298.1668.2201.2961.4001..5477..7609.10670.15089

%C .1064..693..866.1041.1351.1742.2201.2852.3765.4997..6729..9212.12754.17844

%C .1699..992.1229.1473.1881.2382.2961.3765.4870.6337..8374.11265.15355.21197

%C .2734.1418.1746.2086.2623.3267.4001.4997.6337.8086.10481.13841.18550.25229

%H R. H. Hardin, <a href="/A224559/b224559.txt">Table of n, a(n) for n = 1..1566</a>

%F Empirical for diagonal:

%F k=0: a(n) = 6*a(n-1) -15*a(n-2) +23*a(n-3) -30*a(n-4) +36*a(n-5) -34*a(n-6) +27*a(n-7) -21*a(n-8) +13*a(n-9) -6*a(n-10) +3*a(n-11) -a(n-12) for n>14

%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..12+: 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..0..0..0..0..0....1..1..1..1..1..1....1..1..1..1..1..0....1..0..0..0..0..1

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Apr 10 2013

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Last modified December 6 19:17 EST 2021. Contains 349567 sequences. (Running on oeis4.)