A295379 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 2 or 4 1s.

2, 3, 3, 5, 8, 5, 8, 19, 19, 8, 13, 48, 74, 48, 13, 21, 120, 278, 278, 120, 21, 34, 299, 1067, 1634, 1067, 299, 34, 55, 747, 4071, 9507, 9507, 4071, 747, 55, 89, 1865, 15557, 55643, 85310, 55643, 15557, 1865, 89, 144, 4656, 59407, 325134, 761795, 761795, 325134

Offset

1,1

Comments

Table starts

..2....3......5........8........13..........21............34.............55

..3....8.....19.......48.......120.........299...........747...........1865

..5...19.....74......278......1067........4071.........15557..........59407

..8...48....278.....1634......9507.......55643........325134........1900380

.13..120...1067.....9507.....85310......761795.......6819658.......60996884

.21..299...4071....55643....761795....10437240.....142860055.....1956512289

.34..747..15557...325134...6819658...142860055....2995361770....62765357574

.55.1865..59407..1900380..60996884..1956512289...62765357574..2013609204094

.89.4656.226944.11107738.545729054.26790134422.1315649551906.64595519660126

Links

R. H. Hardin, Table of n, a(n) for n = 1..311

Formula

Empirical for column k:

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

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

k=3: [order 10]

k=4: [order 25]

k=5: [order 70]

Example

Some solutions for n=5 k=4
..0..0..0..0. .1..0..1..0. .0..0..1..0. .0..0..0..1. .0..0..1..0
..0..1..0..0. .0..0..0..0. .1..1..0..1. .1..0..0..0. .1..0..0..0
..1..0..0..1. .0..0..0..1. .1..1..1..0. .0..0..0..0. .0..1..0..0
..0..0..1..0. .1..1..0..0. .0..1..1..1. .0..0..0..1. .1..0..0..1
..0..1..0..0. .1..1..0..1. .0..0..1..1. .0..0..1..0. .0..1..0..0

Crossrefs

Column 1 is A000045(n+2).

Column 2 is A295045.

Sequence in context: A296335 A296635 A295051 * A295352 A295606 A154690

Adjacent sequences: A295376 A295377 A295378 * A295380 A295381 A295382

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 21 2017

Status

approved