A224577 - OEIS

A224577

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

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OFFSET

1,1

COMMENTS

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

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..1351

FORMULA

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)

EXAMPLE

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

CROSSREFS

Sequence in context: A343282 A224569 A224570 * A235299 A186013 A102868

Adjacent sequences: A224574 A224575 A224576 * A224578 A224579 A224580

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Apr 10 2013

STATUS

approved