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A224676 T(n,k)=Number of (n+1)X(k+1) 0..2 matrices with each 2X2 subblock idempotent.

%I A224676 #6 Jul 23 2025 05:17:52
%S A224676 12,25,25,41,50,41,70,76,76,70,115,123,108,123,115,189,191,170,170,
%T A224676 191,189,308,300,257,260,257,300,308,501,470,398,381,381,398,470,501,
%U A224676 813,741,617,573,542,573,617,741,813,1318,1173,967,864,793,793,864,967,1173,1318
%N A224676 T(n,k)=Number of (n+1)X(k+1) 0..2 matrices with each 2X2 subblock idempotent.
%C A224676 Table starts
%C A224676 ...12...25...41...70..115..189..308..501...813..1318..2135..3457..5596..9057
%C A224676 ...25...50...76..123..191..300..470..741..1173..1866..2980..4775..7671.12348
%C A224676 ...41...76..108..170..257..398..617..967..1525..2421..3862..6185..9934.15990
%C A224676 ...70..123..170..260..381..573..864.1322..2043..3191..5026..7972.12713.20357
%C A224676 ..115..191..257..381..542..793.1166.1746..2650..4080..6355..9996.15843.25257
%C A224676 ..189..300..398..573..793.1126.1608.2343..3471..5236..8022.12457.19553.30950
%C A224676 ..308..470..617..864.1166.1608.2230.3157..4554..6711.10083.15415.23907.37504
%C A224676 ..501..741..967.1322.1746.2343.3157.4336..6072..8705.12767.19130.29198.45247
%C A224676 ..813.1173.1525.2043.2650.3471.4554.6072..8246.11470.16359.23922.35783.54575
%C A224676 .1318.1866.2421.3191.4080.5236.6711.8705.11470.15458.21373.30371.44312.66212
%H A224676 R. H. Hardin, <a href="/A224676/b224676.txt">Table of n, a(n) for n = 1..967</a>
%F A224676 Empirical for column k:
%F A224676 k=1: a(n) = 2*a(n-1) -a(n-3)
%F A224676 k=2: a(n) = 4*a(n-1) -5*a(n-2) +a(n-3) +2*a(n-4) -a(n-5)
%F A224676 k=3..7+: a(n) = 4*a(n-1) -5*a(n-2) +a(n-3) +2*a(n-4) -a(n-5) for n>6
%e A224676 Some solutions for n=3 k=4
%e A224676 ..1..1..1..1..0....1..0..1..0..2....1..0..1..0..0....0..1..0..0..2
%e A224676 ..0..0..0..0..0....1..0..1..0..1....1..0..1..0..1....0..1..0..0..1
%e A224676 ..0..0..0..0..0....1..0..1..0..1....1..0..1..0..1....0..1..0..0..1
%e A224676 ..0..0..1..1..1....0..0..1..0..1....1..0..1..0..1....0..1..0..0..1
%Y A224676 Diagonal is A224659(n+1)
%K A224676 nonn,tabl
%O A224676 1,1
%A A224676 _R. H. Hardin_ Apr 14 2013