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A286209 Number of n X 1 0..1 arrays with the number of 1's king-move adjacent to some 0 two less than the number of 0's adjacent to some 1. 6
0, 0, 0, 0, 0, 0, 1, 3, 10, 24, 60, 134, 304, 656, 1420, 2996, 6312, 13112, 27167, 55825, 114412, 233282, 474563, 962159, 1947098, 3931288, 7925708, 15952866, 32072580, 64404708, 129213082, 259009006, 518818124, 1038549912, 2077775396, 4154785904, 8304424080 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..3327 (terms n = 1..210 from R. H. Hardin)

EXAMPLE

All solutions for n=7

..0. .0. .0

..1. .0. .1

..0. .1. .0

..0. .0. .0

..0. .0. .1

..1. .1. .0

..0. .0. .0

MAPLE

b:= proc(n, t, h, c) option remember; `if`(abs(c-2)>n, 0, `if`(n=0, 1,

b(n-1, [1, 3, 1][t], 2, c-`if`(h=3, 1, 0))+

b(n-1, 2, [1, 3, 1][h], c+`if`(t=3, 1, 0))))

end:

a:= n-> b(n, 1$2, 0):

seq(a(n), n=0..40); # Alois P. Heinz, Apr 29 2019

MATHEMATICA

b[n_, t_, h_, c_] := b[n, t, h, c] = If[Abs[c - 2] > n, 0, If[n == 0, 1,

b[n - 1, {1, 3, 1}[[t]], 2, c - If[h == 3, 1, 0]] +

b[n - 1, 2, {1, 3, 1}[[h]], c + If[t == 3, 1, 0]]]];

a[n_] := b[n, 1, 1, 0];

Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Jun 27 2022, after Alois P. Heinz *)

CROSSREFS

Column k=1 of A286216.

Column k=2 of A307796.

Sequence in context: A338706 A338710 A336516 * A293797 A179608 A340686

Adjacent sequences: A286206 A286207 A286208 * A286210 A286211 A286212

KEYWORD

nonn

AUTHOR

R. H. Hardin, May 04 2017

STATUS

approved

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Last modified February 8 01:34 EST 2023. Contains 360133 sequences. (Running on oeis4.)