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A304926 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 5 or 7 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 4, 4, 4, 8, 5, 5, 8, 16, 9, 15, 9, 16, 32, 22, 31, 31, 22, 32, 64, 45, 73, 87, 73, 45, 64, 128, 101, 191, 266, 266, 191, 101, 128, 256, 218, 466, 851, 1054, 851, 466, 218, 256, 512, 477, 1125, 2510, 4186, 4186, 2510, 1125, 477, 512, 1024, 1041, 2762, 7348, 16158 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

...1...2....4.....8.....16......32.......64.......128........256.........512

...2...4....5.....9.....22......45......101.......218........477........1041

...4...5...15....31.....73.....191......466......1125.......2762........6805

...8...9...31....87....266.....851.....2510......7348......21910.......65581

..16..22...73...266...1054....4186....16158.....63555.....251536......988178

..32..45..191...851...4186...21214...104451....524286....2629697....13159898

..64.101..466..2510..16158..104451...649029...4123792...26044218...164807242

.128.218.1125..7348..63555..524286..4123792..33757130..273455401..2220694647

.256.477.2762.21910.251536.2629697.26044218.273455401.2831764125.29378878160

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..337

FORMULA

Empirical for column k:

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

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

k=3: a(n) = a(n-1) +2*a(n-2) +4*a(n-3) +2*a(n-4) -2*a(n-5) -7*a(n-6) -6*a(n-7) for n>9

k=4: [order 13] for n>18

k=5: [order 34] for n>41

k=6: [order 96] for n>103

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000079(n-1).

Column 2 is A052962 for n>2.

Sequence in context: A305340 A304604 A316420 * A306166 A317383 A033717

Adjacent sequences:  A304923 A304924 A304925 * A304927 A304928 A304929

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, May 21 2018

STATUS

approved

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Last modified January 18 10:47 EST 2022. Contains 350454 sequences. (Running on oeis4.)