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

allocated for R. H. Hardin

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

96608, 18044, 18044, 16696, 5668, 16696, 18868, 5696, 5696, 18868, 22096, 6411, 5896, 6411, 22096, 25769, 7034, 6659, 6659, 7034, 25769, 28708, 7386, 7295, 7394, 7295, 7386, 28708, 33705, 7843, 7884, 8143, 8143, 7884, 7843, 33705, 40120, 9237

1,1

Table starts

.96608.18044.16696.18868.22096.25769.28708.33705.40120.50747.67088.91787.125249

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

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

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

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

.25769..7386..7884..8714..9480.10086.10561.12373.15413.19404.24072.29230..34734

.28708..7843..8294..9164..9946.10561.11032.12921.16072.20202.25024.30332..35979

.33705..9237..9831.10807.11672.12373.12921.14984.18329.22663.27712.33261..39146

.40120.11797.12556.13624.14594.15413.16072.18329.21920.26498.31808.37632..43791

.50747.15264.16161.17332.18457.19404.20202.22663.26498.31362.36961.43072..49535

Empirical for column k:

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

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

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

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

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

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

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

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

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

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

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

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

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

Some solutions for n=2 k=4

..0..0..1..0..0..0..0..0..0....1..0..0..0..0..0..0..0..0

..0..0..1..0..0..0..0..0..1....1..0..0..0..0..0..0..0..0

..0..0..1..0..0..0..0..0..1....1..0..0..0..0..0..0..0..0

..0..0..1..0..0..0..0..0..0....1..0..0..0..0..0..0..0..0

..0..0..1..0..0..0..0..0..1....1..0..0..0..0..0..0..0..0

..0..0..1..0..0..0..0..0..1....1..0..0..0..0..0..0..0..0

..0..0..1..0..0..0..0..0..1....0..0..0..0..0..1..1..1..1

allocated

nonn,tabl

R. H. Hardin Apr 10 2013

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