The On-Line Encyclopedia of Integer Sequences (OEIS)

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A318040

Number of nX3 0..1 arrays with every element unequal to 0, 2, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
(history; published version)

#4 by R. H. Hardin at Mon Aug 13 14:30:24 EDT 2018

STATUS

editing

approved

#3 by R. H. Hardin at Mon Aug 13 14:30:21 EDT 2018

LINKS

R. H. Hardin, <a href="/A318040/b318040.txt">Table of n, a(n) for n = 1..210</a>

#2 by R. H. Hardin at Mon Aug 13 14:30:05 EDT 2018

NAME

allocated for R. H. Hardin

Number of nX3 0..1 arrays with every element unequal to 0, 2, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

DATA

1, 2, 8, 21, 86, 377, 1648, 7261, 31969, 140758, 619822, 2729394, 12018832, 52924798, 233054021, 1026252071, 4519095292, 19899811452, 87628711701, 385872557006, 1699187715083, 7482363905416, 32948548958936, 145088757010002

OFFSET

1,2

COMMENTS

Column 3 of A318045.

FORMULA

Empirical: a(n) = 7*a(n-1) -15*a(n-2) +21*a(n-3) -25*a(n-4) +6*a(n-5) +9*a(n-6) -22*a(n-7) +44*a(n-8) -16*a(n-9) +32*a(n-10) -20*a(n-11) -31*a(n-12) -a(n-13) +2*a(n-14) -2*a(n-15) -18*a(n-16) +3*a(n-17) +12*a(n-18) +14*a(n-19) +3*a(n-20) -2*a(n-21) for n>23

EXAMPLE

Some solutions for n=5

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

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

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

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

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

CROSSREFS

Cf. A318045.

KEYWORD

allocated

nonn

AUTHOR

R. H. Hardin, Aug 13 2018

STATUS

approved

editing

#1 by R. H. Hardin at Mon Aug 13 14:28:01 EDT 2018

NAME

allocated for R. H. Hardin

KEYWORD

allocated

STATUS

approved