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A204076 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock having equal diagonal elements or equal antidiagonal elements, and new values 0..2 introduced in row major order 8
8, 38, 38, 188, 329, 188, 938, 2882, 2882, 938, 4688, 25277, 45056, 25277, 4688, 23438, 221726, 706454, 706454, 221726, 23438, 117188, 1944977, 11081828, 19934369, 11081828, 1944977, 117188, 585938, 17061338, 173848010, 563880962, 563880962 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

......8........38.........188............938.............4688

.....38.......329........2882..........25277...........221726

....188......2882.......45056.........706454.........11081828

....938.....25277......706454.......19934369........563880962

...4688....221726....11081828......563880962......28864215128

..23438...1944977...173848010....15960507749....1480470688070

.117188..17061338..2727300008...451830740558...75985220860460

.585938.149662085.42785526110.12791537916233.3900809853901802

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..220

FORMULA

Empirical for column k:

k=1: a(n) = (3*5^n+1)/2

k=2: a(n) = 10*a(n-1) -11*a(n-2) +2*a(n-3)

k=3: a(n) = 20*a(n-1) -73*a(n-2) +86*a(n-3) -32*a(n-4)

k=4: a(n) = 32*a(n-1) -55*a(n-2) -1588*a(n-3) +5428*a(n-4) -2664*a(n-5) -3936*a(n-6) +3040*a(n-7) -256*a(n-8)

k=5: (order 13 recurrence)

k=6: (order 29 recurrence)

k=7: (order 55 recurrence)

EXAMPLE

Some solutions for n=4 k=3

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

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

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

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

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

CROSSREFS

Column 1 is A199213

Sequence in context: A201452 A128246 A257215 * A319960 A163832 A139798

Adjacent sequences:  A204073 A204074 A204075 * A204077 A204078 A204079

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Jan 10 2012

STATUS

approved

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Last modified November 17 18:42 EST 2018. Contains 317276 sequences. (Running on oeis4.)