A251149 T(n,k) = Number of (n+1) X (k+1) 0..2 arrays with every 2 X 2 subblock summing to 4 and no 2 X 2 subblock having exactly two nonzero entries.

13, 27, 27, 53, 49, 53, 107, 87, 87, 107, 213, 161, 143, 161, 213, 427, 299, 247, 247, 299, 427, 853, 565, 433, 401, 433, 565, 853, 1707, 1075, 777, 667, 667, 777, 1075, 1707, 3413, 2065, 1413, 1141, 1061, 1141, 1413, 2065, 3413, 6827, 3991, 2607, 1987, 1743

Offset

1,1

Comments

Table starts:

...13...27...53...107...213...427...853..1707..3413...6827..13653..27307..54613

...27...49...87...161...299...565..1075..2065..3991...7761..15163..29749..58563

...53...87..143...247...433...777..1413..2607..4863...9167..17433..33417..64493

..107..161..247...401...667..1141..1987..3521..6327..11521..21227..39541..74387

..213..299..433...667..1061..1743..2925..5003..8689..15307..27317..49359..90237

..427..565..777..1141..1743..2763..4491..7453.12569..21501..37255..65355.116035

..853.1075.1413..1987..2925..4491..7101.11491.18917..31587..53389..91275.157789

.1707.2065.2607..3521..5003..7453.11491.18193.29359..48081..79675.133405.225555

.3413.3991.4863..6327..8689.12569.18917.29359.46575..75087.122521.201881.335501

.6827.7761.9167.11521.15307.21501.31587.48081.75087.119441.192507.313341.514067

Links

R. H. Hardin, Table of n, a(n) for n = 1..364

Formula

Empirical for column k:

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

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

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

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

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

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

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

Example

Some solutions for n=4, k=4:
..0..1..0..2..1....1..0..1..1..1....1..0..1..1..2....2..1..2..1..1
..1..2..1..1..0....1..2..1..1..1....1..2..1..1..0....0..1..0..1..1
..1..0..1..1..2....1..0..1..1..1....0..1..0..2..1....1..2..1..2..0
..1..2..1..1..0....1..2..1..1..1....1..2..1..1..0....0..1..0..1..1
..1..0..1..1..2....1..0..1..1..1....0..1..0..2..1....2..1..2..1..1

Crossrefs

Column 1 is A048573(n+2).

Sequence in context: A098961 A033897 A005029 * A293787 A041330 A041765

Adjacent sequences: A251146 A251147 A251148 * A251150 A251151 A251152

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 30 2014

Status

approved