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, 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

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 A362492

Adjacent sequences: A204073 A204074 A204075 * A204077 A204078 A204079

Keyword

nonn,tabl

Author

R. H. Hardin Jan 10 2012

Status

approved