A229428 - OEIS

A229428

T(n,k) = Number of n X k 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, rows lexicographically nondecreasing, and columns lexicographically nonincreasing.

3, 5, 5, 8, 12, 8, 12, 27, 27, 12, 17, 55, 83, 55, 17, 23, 102, 222, 222, 102, 23, 30, 175, 524, 754, 524, 175, 30, 38, 282, 1116, 2204, 2204, 1116, 282, 38, 47, 432, 2187, 5700, 7816, 5700, 2187, 432, 47, 57, 635, 4005, 13345, 24126, 24126, 13345, 4005, 635, 57

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OFFSET

1,1

COMMENTS

Table starts

..3...5....8....12.....17.....23......30.......38.......47........57........68

..5..12...27....55....102....175.....282......432......635.......902......1245

..8..27...83...222....524...1116....2187.....4005.....6936.....11465.....18219

.12..55..222...754...2204...5700...13345....28794....58053....110550....200533

.17.102..524..2204...7816..24126...66503...166972...387738....842802...1731129

.23.175.1116..5700..24126..87648..281016...812352..2152643...5297329..12231874

.30.282.2187.13345..66503.281016.1037193..3420692.10260128..28379127..73192023

.38.432.4005.28794.166972.812352.3420692.12768612.43042290.132960319.380811699

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..480

FORMULA

Empirical for column k:

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

k=2: a(n) = (1/24)*n^4 + (5/12)*n^3 + (11/24)*n^2 + (25/12)*n + 2, A229422

k=3: [polynomial of degree 6], A229423

k=4: [polynomial of degree 8], A229424

k=5: [polynomial of degree 10], A229425

k=6: [polynomial of degree 12], A229426

k=7: [polynomial of degree 14]

EXAMPLE

Some solutions for n=4 k=4

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

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

..2..2..1..1....2..1..1..1....2..1..1..1....2..2..2..1....2..2..1..1

..2..2..2..1....2..1..1..1....2..2..1..1....2..2..2..2....2..2..2..1

CROSSREFS

Column 1 is A022856(n+4).

Main diagonal is A229421.

Sequence in context: A063285 A316938 A112507 * A348374 A029639 A087349

Adjacent sequences: A229425 A229426 A229427 * A229429 A229430 A229431

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Sep 22 2013

STATUS

approved