The On-Line Encyclopedia of Integer Sequences (OEIS)

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A204417

T(n,k)=Number of (n+2)X(k+2) 0..2 arrays with every 3X3 subblock having three strictly increasing elements in a row horizontally or vertically, exactly one way
(history; published version)

#5 by Russ Cox at Sat Mar 31 12:37:01 EDT 2012

AUTHOR

_R. H. Hardin (rhhardin(AT)att.net) _ Jan 15 2012

Discussion

Sat Mar 31

12:37

OEIS Server: https://oeis.org/edit/global/875

#4 by Ron Hardin at Sun Jan 15 11:59:49 EST 2012

STATUS

editing

approved

#3 by Ron Hardin at Sun Jan 15 11:59:33 EST 2012

LINKS

R. H. Hardin, <a href="/A204417/b204417.txt">Table of n, a(n) for n = 1..924</a>

#2 by Ron Hardin at Sun Jan 15 11:59:06 EST 2012

NAME

allocated for Ron HardinT(n,k)=Number of (n+2)X(k+2) 0..2 arrays with every 3X3 subblock having three strictly increasing elements in a row horizontally or vertically, exactly one way

DATA

3570, 34274, 34274, 423416, 154938, 423416, 2827014, 781884, 781884, 2827014, 22956524, 5597126, 947990, 5597126, 22956524, 254913953, 52039032, 5776350, 5776350, 52039032, 254913953, 2004465237, 395943745, 49914501, 11785518

OFFSET

1,1

COMMENTS

Table starts

........3570.......34274......423416.....2827014....22956524....254913953

.......34274......154938......781884.....5597126....52039032....395943745

......423416......781884......947990.....5776350....49914501....422397021

.....2827014.....5597126.....5776350....11785518....89459577...1122887052

....22956524....52039032....49914501....89459577...253954944...1364559057

...254913953...395943745...422397021..1122887052..1364559057...2050960896

..2004465237..2826265830..3619976949..6016853259..8802512928..13168291392

.15823989959.26252359826.29207652750.53009843553.94119917760.115434720000

FORMULA

Empirical for column k:

k=1: (order 14 recurrence)

k=2: (order 19 recurrence for n>22)

k=3: a(n) = 577*a(n-3) +63*a(n-5) -63*a(n-8) for n>16

k=4: a(n) = 577*a(n-3) for n>15

k=5: a(n) = 577*a(n-3) for n>16

k=6: a(n) = 577*a(n-3) for n>17

k=7: a(n) = 577*a(n-3) for n>18

EXAMPLE

Some solutions for n=3 k=3

..0..0..2..2..2....2..2..0..0..2....0..0..2..0..1....1..2..2..1..0

..0..1..0..1..2....2..1..0..1..0....0..0..0..1..0....0..0..1..2..1

..1..2..2..1..0....0..1..2..2..1....0..1..2..2..1....0..1..2..1..2

..2..0..1..2..1....0..0..1..2..2....1..0..1..2..2....1..1..0..1..2

..0..1..2..1..2....0..1..0..1..2....0..1..0..1..2....0..0..1..2..0

KEYWORD

allocated

nonn,tabl

AUTHOR

R. H. Hardin (rhhardin(AT)att.net) Jan 15 2012

STATUS

approved

editing

#1 by Ron Hardin at Sun Jan 15 11:50:05 EST 2012

NAME

allocated for Ron Hardin

KEYWORD

allocated

STATUS

approved