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 A224577 T(n,k)=Number of (n+5)X(k+5) 0..1 matrices with each 6X6 subblock idempotent 9

%I #4 Apr 10 2013 18:39:04

%S 96608,18044,18044,16696,5668,16696,18868,5696,5696,18868,22096,6411,

%T 5896,6411,22096,25769,7034,6659,6659,7034,25769,28708,7386,7295,7394,

%U 7295,7386,28708,33705,7843,7884,8143,8143,7884,7843,33705,40120,9237

%N T(n,k)=Number of (n+5)X(k+5) 0..1 matrices with each 6X6 subblock idempotent

%C Table starts

%C .96608.18044.16696.18868.22096.25769.28708.33705.40120.50747.67088.91787.125249

%C .18044..5668..5696..6411..7034..7386..7843..9237.11797.15264.19346.23731..28733

%C .16696..5696..5896..6659..7295..7884..8294..9831.12556.16161.20310.25054..30119

%C .18868..6411..6659..7394..8143..8714..9164.10807.13624.17332.21731.26592..31785

%C .22096..7034..7295..8143..8880..9480..9946.11672.14594.18457.22982.27995..33345

%C .25769..7386..7884..8714..9480.10086.10561.12373.15413.19404.24072.29230..34734

%C .28708..7843..8294..9164..9946.10561.11032.12921.16072.20202.25024.30332..35979

%C .33705..9237..9831.10807.11672.12373.12921.14984.18329.22663.27712.33261..39146

%C .40120.11797.12556.13624.14594.15413.16072.18329.21920.26498.31808.37632..43791

%C .50747.15264.16161.17332.18457.19404.20202.22663.26498.31362.36961.43072..49535

%H R. H. Hardin, <a href="/A224577/b224577.txt">Table of n, a(n) for n = 1..1351</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1) -2*a(n-2) +2*a(n-3) -a(n-4) +2*a(n-6) -3*a(n-7) +4*a(n-8) -4*a(n-9) +3*a(n-10) -2*a(n-11) -2*a(n-14) +2*a(n-15) -2*a(n-16) +2*a(n-17) -a(n-18) +a(n-19) for n>30

%F k=2: a(n) = 2*a(n-1) -2*a(n-2) +2*a(n-3) -2*a(n-4) +3*a(n-5) -2*a(n-6) +a(n-7) -a(n-9) +a(n-10) -3*a(n-11) +3*a(n-12) -4*a(n-13) +3*a(n-14) -2*a(n-15) +2*a(n-16) -a(n-17) +a(n-18) +a(n-19) -a(n-20) +a(n-21) -a(n-22) +a(n-23) -a(n-24) for n>33

%F k=3: a(n) = 3*a(n-1) -4*a(n-2) +4*a(n-3) -3*a(n-4) +a(n-5) +2*a(n-6) -5*a(n-7) +6*a(n-8) -6*a(n-9) +4*a(n-10) -a(n-11) -a(n-12) +2*a(n-13) -2*a(n-14) +2*a(n-15) -a(n-16) for n>21

%F k=4: a(n) = 3*a(n-1) -4*a(n-2) +4*a(n-3) -3*a(n-4) +a(n-5) +2*a(n-6) -5*a(n-7) +6*a(n-8) -6*a(n-9) +4*a(n-10) -a(n-11) -a(n-12) +2*a(n-13) -2*a(n-14) +2*a(n-15) -a(n-16) for n>20

%F k=5: a(n) = 4*a(n-1) -6*a(n-2) +3*a(n-3) +3*a(n-4) -6*a(n-5) +5*a(n-6) -4*a(n-7) +3*a(n-8) -3*a(n-10) +3*a(n-11) -a(n-12) for n>16

%F k=6: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +2*a(n-6) -5*a(n-7) +4*a(n-8) -a(n-9) -a(n-12) +2*a(n-13) -a(n-14) for n>18

%F k=7: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +2*a(n-6) -5*a(n-7) +4*a(n-8) -a(n-9) -a(n-12) +2*a(n-13) -a(n-14) for n>18

%F k=8: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +2*a(n-6) -5*a(n-7) +4*a(n-8) -a(n-9) -a(n-12) +2*a(n-13) -a(n-14) for n>18

%F k=9: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +2*a(n-6) -5*a(n-7) +4*a(n-8) -a(n-9) -a(n-12) +2*a(n-13) -a(n-14) for n>18

%F k=10: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +2*a(n-6) -5*a(n-7) +4*a(n-8) -a(n-9) -a(n-12) +2*a(n-13) -a(n-14) for n>18

%F k=11: a(n) = 4*a(n-1) -6*a(n-2) +3*a(n-3) +3*a(n-4) -6*a(n-5) +5*a(n-6) -4*a(n-7) +3*a(n-8) -3*a(n-10) +3*a(n-11) -a(n-12) for n>16

%F k=12: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +2*a(n-6) -5*a(n-7) +4*a(n-8) -a(n-9) -a(n-12) +2*a(n-13) -a(n-14) for n>18

%F (note: the larger repeated k>=6 formula also works for k=11)

%e Some solutions for n=2 k=4

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

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

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Apr 10 2013

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Last modified December 4 07:54 EST 2023. Contains 367557 sequences. (Running on oeis4.)