A251258 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every 2X2 subblock having a single 1 or two 1s on the same edge

8, 18, 18, 38, 56, 38, 84, 150, 150, 84, 180, 446, 464, 446, 180, 394, 1232, 1770, 1770, 1232, 394, 850, 3602, 5680, 9130, 5680, 3602, 850, 1852, 10108, 21088, 38332, 38332, 21088, 10108, 1852, 4008, 29272, 69270, 192442, 185620, 192442, 69270, 29272, 4008

Offset

1,1

Comments

Table starts

....8.....18......38.......84........180.........394..........850

...18.....56.....150......446.......1232........3602........10108

...38....150.....464.....1770.......5680.......21088........69270

...84....446....1770.....9130......38332......192442.......836546

..180...1232....5680....38332.....185620.....1215600......6080510

..394...3602...21088...192442....1215600....10753448.....71459218

..850..10108...69270...836546....6080510....71459218....539961360

.1852..29272..252226..4112126...38748690...612889014...6151714502

.4008..82854..842160.18298862..198765264..4229034766..47962536500

.8714.238640.3024532.88585834.1238605998.35355603854.531311887046

Links

R. H. Hardin, Table of n, a(n) for n = 1..611

Formula

Empirical for column k:

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

k=2: a(n) = 3*a(n-1) +4*a(n-2) -14*a(n-3) +3*a(n-4) +3*a(n-5)

k=3: a(n) = a(n-1) +13*a(n-2) -7*a(n-3) -32*a(n-4) +8*a(n-5) +10*a(n-6)

k=4: [order 12]

k=5: [order 17]

k=6: [order 31]

k=7: [order 49]

Example

Some solutions for n=4 k=4
..0..1..0..0..0....0..0..1..0..0....0..0..1..0..1....1..0..1..1..0
..0..1..0..1..1....1..0..1..0..1....1..0..0..0..0....1..0..0..0..0
..0..0..0..0..0....0..0..0..0..0....0..0..1..0..1....1..0..1..1..0
..1..1..1..0..1....0..1..0..1..0....1..0..1..0..0....1..0..0..0..0
..0..0..0..0..1....0..1..0..1..0....0..0..1..0..1....1..0..1..1..0

Crossrefs

Sequence in context: A322031 A196207 A196474 * A101241 A307973 A031258

Adjacent sequences: A251255 A251256 A251257 * A251259 A251260 A251261

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 01 2014

Status

approved