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A299595 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero. 7
1, 2, 2, 3, 1, 3, 5, 3, 3, 5, 8, 5, 5, 5, 8, 13, 8, 11, 11, 8, 13, 21, 15, 19, 23, 19, 15, 21, 34, 26, 35, 53, 53, 35, 26, 34, 55, 45, 65, 121, 113, 121, 65, 45, 55, 89, 80, 120, 250, 256, 256, 250, 120, 80, 89, 144, 140, 220, 533, 541, 576, 541, 533, 220, 140, 144, 233, 245 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

..1..2...3....5....8...13....21....34....55.....89....144....233.....377

..2..1...3....5....8...15....26....45....80....140....245....431.....756

..3..3...5...11...19...35....65...120...220....404....744...1369....2517

..5..5..11...23...53..121...250...533..1162...2490...5327..11465...24641

..8..8..19...53..113..256...541..1148..2488...5349..11453..24617...52916

.13.15..35..121..256..576..1225..2601..5625..12100..25921..55696..119716

.21.26..65..250..541.1225..2583..5488.11899..25570..54750.117697..252985

.34.45.120..533.1148.2601..5488.11656.25269..54309.116285.249968..537305

.55.80.220.1162.2488.5625.11899.25269.54738.117679.252010.541648.1164265

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..9934

FORMULA

Empirical for diagonal: [linear recurrence of order 15] for n>18

Empirical for column k:

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

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

k=3: a(n) = a(n-1) +2*a(n-3) +a(n-4) +a(n-5) for n>8

k=4..99: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4) -a(n-5) -a(n-6) for n>9

EXAMPLE

Some solutions for n=5 k=4

..0..0..1..0. .0..1..0..0. .0..1..0..0. .0..0..0..0. .0..0..0..0

..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..1. .1..0..0..0

..0..0..0..0. .0..0..0..0. .0..0..0..1. .0..0..0..0. .0..0..0..0

..1..0..0..1. .1..0..0..0. .1..0..0..0. .1..0..0..0. .0..0..0..1

..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..1..0. .0..0..0..0

CROSSREFS

Column 1 is A000045(n+1).

Column 2 is A193147.

Sequence in context: A325821 A341607 A303719 * A304270 A318545 A071450

Adjacent sequences:  A299592 A299593 A299594 * A299596 A299597 A299598

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Feb 13 2018

STATUS

approved

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Last modified January 25 10:12 EST 2022. Contains 350565 sequences. (Running on oeis4.)