login
T(n,k)=Number of (n+6)X(k+6) 0..1 matrices with each 7X7 subblock idempotent
9

%I #4 Apr 11 2013 08:52:41

%S 2185738,164935,164935,125525,26918,125525,122508,22928,22928,122508,

%T 128620,24643,21966,24643,128620,138581,26542,24293,24293,26542,

%U 138581,146715,27611,26294,26528,26294,27611,146715,156428,28629,27945,28783

%N T(n,k)=Number of (n+6)X(k+6) 0..1 matrices with each 7X7 subblock idempotent

%C Table starts

%C .2185738.164935.125525.122508.128620.138581.146715.156428.171787.199628.251449

%C ..164935..26918..22928..24643..26542..27611..28629..29006..34239..43678..55912

%C ..125525..22928..21966..24293..26294..27945..29066..30031..35282..44719..57279

%C ..122508..24643..24293..26528..28783..30456..31741..32736..38059..47654..60745

%C ..128620..26542..26294..28783..31062..32814..34107..35087..40536..50460..63767

%C ..138581..27611..27945..30456..32814..34588..35891..36872..42492..52620..66173

%C ..146715..28629..29066..31741..34107..35891..37202..38192..43958..54300..68099

%C ..156428..29006..30031..32736..35087..36872..38192..39188..45101..55656..69702

%C ..171787..34239..35282..38059..40536..42492..43958..45101..51306..62221..76663

%C ..199628..43678..44719..47654..50460..52620..54300..55656..62221..73564..88470

%H R. H. Hardin, <a href="/A224588/b224588.txt">Table of n, a(n) for n = 1..1055</a>

%F Empirical for column k:

%F k=1: [order 27] for n>39

%F k=2: [order 29] for n>39

%F k=3: [order 25] for n>33

%F k=4: [order 17] for n>23

%F k=5: [order 15] for n>21

%F k=6: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +3*a(n-4) -a(n-5) +a(n-7) -2*a(n-8) +2*a(n-10) -a(n-11) for n>17

%F k=7..15+: a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4) +a(n-7) -3*a(n-8) +3*a(n-9) -a(n-10) for n>16

%e Some solutions for n=2 k=4

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

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

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

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Apr 11 2013