The On-Line Encyclopedia of Integer Sequences (OEIS)

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Number of nX3 0..1 arrays with every element equal to 1, 2, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
(history; published version)

#4 by R. H. Hardin at Thu Apr 12 10:51:46 EDT 2018

STATUS

editing

approved

#3 by R. H. Hardin at Thu Apr 12 10:51:44 EDT 2018

LINKS

R. H. Hardin, <a href="/A302724/b302724.txt">Table of n, a(n) for n = 1..210</a>

#2 by R. H. Hardin at Thu Apr 12 10:51:21 EDT 2018

NAME

allocated for R. H. Hardin

Number of nX3 0..1 arrays with every element equal to 1, 2, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

DATA

1, 7, 22, 83, 301, 1079, 4064, 15183, 55012, 207349, 770421, 2830250, 10617371, 39400644, 145704104, 544623685, 2020998479, 7497256552, 27957348859, 103787074017, 385563034716, 1435728019366, 5332352333196, 19821039046245

OFFSET

1,2

COMMENTS

Column 3 of A302728.

FORMULA

Empirical: a(n) = 2*a(n-1) +5*a(n-2) +27*a(n-3) -64*a(n-4) -67*a(n-5) +25*a(n-6) -22*a(n-7) -66*a(n-8) -240*a(n-9) +232*a(n-10) +168*a(n-11) -16*a(n-12) +64*a(n-13) +64*a(n-14) +256*a(n-15) -256*a(n-16)

EXAMPLE

Some solutions for n=5

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

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

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

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

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

CROSSREFS

Cf. A302728.

KEYWORD

allocated

nonn

AUTHOR

R. H. Hardin, Apr 12 2018

STATUS

approved

editing

#1 by R. H. Hardin at Thu Apr 12 10:50:10 EDT 2018

NAME

allocated for R. H. Hardin

KEYWORD

allocated

STATUS

approved