A297733 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2 or 4 neighboring 1s.

1, 1, 1, 1, 2, 1, 1, 8, 3, 1, 1, 15, 17, 4, 1, 1, 32, 34, 39, 6, 1, 1, 61, 92, 93, 151, 9, 1, 1, 145, 223, 362, 502, 385, 13, 1, 1, 297, 700, 1103, 2719, 1443, 1026, 19, 1, 1, 658, 1747, 4795, 11341, 11171, 4676, 3272, 28, 1, 1, 1352, 4931, 15646, 82549, 65215, 53173, 19601

Offset

1,5

Comments

Table starts

.1..1....1.....1.......1........1.........1...........1............1

.1..2....8....15......32.......61.......145.........297..........658

.1..3...17....34......92......223.......700........1747.........4931

.1..4...39....93.....362.....1103......4795.......15646........61063

.1..6..151...502....2719....11341.....82549......396787......2346541

.1..9..385..1443...11171....65215....673171.....4414693.....36515720

.1.13.1026..4676...53173...414651...6241242....56834907....675663465

.1.19.3272.19601..304157..3199929..74469526...959915987..16537401517

.1.28.8945.62749.1417699.21221319.718454750.13045679082.322119198752

Links

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

Formula

Empirical for column k:

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

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

k=3: a(n) = a(n-1) +a(n-2) +13*a(n-3) -2*a(n-4) +4*a(n-5) -11*a(n-6) -3*a(n-7) -a(n-8)

k=4: [order 19]

k=5: [order 35]

Empirical for row n:

n=1: a(n) = a(n-1)

n=2: a(n) = 2*a(n-1) +a(n-2) -3*a(n-3) +6*a(n-4) -6*a(n-5)

n=3: [order 9]

n=4: [order 27]

n=5: [order 80]

Example

Some solutions for n=6 k=4
..0..0..0..0. .0..1..1..1. .0..0..0..0. .0..0..1..0. .0..0..1..1
..0..0..0..0. .0..0..1..0. .0..0..1..1. .0..1..0..1. .0..0..1..1
..0..0..1..1. .0..1..1..1. .0..1..1..0. .0..0..1..1. .0..0..0..0
..0..0..1..1. .0..0..0..0. .0..0..0..0. .0..1..1..0. .0..0..0..0
..0..1..0..1. .0..0..1..1. .0..1..1..0. .0..0..0..0. .0..0..1..1
..0..0..1..0. .0..0..1..1. .1..1..0..0. .0..0..0..0. .0..1..1..0

Crossrefs

Column 2 is A000930(n+1).

Sequence in context: A119418 A077058 A053373 * A255812 A249141 A353953

Adjacent sequences: A297730 A297731 A297732 * A297734 A297735 A297736

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 04 2018

Status

approved