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A302528 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero. 12
0, 1, 0, 1, 3, 0, 2, 7, 10, 0, 3, 10, 28, 23, 0, 5, 27, 42, 115, 61, 0, 8, 45, 100, 168, 497, 162, 0, 13, 98, 290, 539, 902, 2086, 421, 0, 21, 193, 730, 1977, 3683, 3256, 9091, 1103, 0, 34, 379, 1700, 5942, 23909, 17546, 15852, 40575, 2890, 0, 55, 778, 4246, 16733, 128242 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Table starts

.0....1......1......2.......3.........5..........8..........13...........21

.0....3......7.....10......27........45.........98.........193..........379

.0...10.....28.....42.....100.......290........730........1700.........4246

.0...23....115....168.....539......1977.......5942.......16733........49219

.0...61....497....902....3683.....23909.....128242......465323......1918153

.0..162...2086...3256...17546....182773....1275348.....5557469.....29725028

.0..421...9091..15852...92603...1551340...16130212....82774516....506265517

.0.1103..40575..77904..615351..18089458..303355178..1916999716..16636194027

.0.2890.172996.314276.3268978.155010391.3654880956.27228654766.305442540368

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..180

FORMULA

Empirical for column k:

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

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

k=3: [order 18]

k=4: [order 72]

Empirical for row n:

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

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

n=3: [order 15] for n>17

n=4: [order 68] for n>69

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 2 is A185828.

Row 1 is A000045(n-1).

Row 2 is A302279.

Sequence in context: A223139 A302278 A302728 * A303410 A126671 A209437

Adjacent sequences:  A302525 A302526 A302527 * A302529 A302530 A302531

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Apr 09 2018

STATUS

approved

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Last modified January 27 08:21 EST 2022. Contains 350606 sequences. (Running on oeis4.)