

A206839


Number of 1 X n 0..3 arrays avoiding the pattern z2 z1 z in any row, column, nwtose diagonal or netosw antidiagonal.


4



1, 4, 16, 62, 241, 936, 3636, 14124, 54865, 213124, 827884, 3215930, 12492337, 48526704, 188502840, 732242616, 2844409393, 11049158596, 42920651992, 166726031798, 647650219393, 2515808732184, 9772703517132, 37962239661540, 147464991401185, 572830367302660
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OFFSET

0,2


COMMENTS

Column and row 1 of A206838.


LINKS

R. H. Hardin and Alois P. Heinz, Table of n, a(n) for n = 0..1000 (terms n = 1..210 from R. H. Hardin)
Index entries for linear recurrences with constant coefficients, signature (4,0,2,1).


FORMULA

a(n) = 4*a(n1) 2*a(n3) +a(n4).
G.f.: 1 / (1  4*x + 2*x^3  x^4).  Colin Barker, Jul 05 2019


EXAMPLE

Some solutions for n=5
..3..1..2..1..0....1..0..0..0..0....2..2..1..1..0....1..1..3..3..0


MAPLE

a:= n> (<<0100>, <0010>, <0001>, <1204>>^n)[4$2]:
seq(a(n), n=0..25); # Alois P. Heinz, Oct 26 2016


PROG

(PARI) Vec(1 / (1  4*x + 2*x^3  x^4) + O(x^26)) \\ Colin Barker, Jul 05 2019


CROSSREFS

Cf. A206838.
Sequence in context: A172025 A171278 A227438 * A244827 A169760 A222699
Adjacent sequences: A206836 A206837 A206838 * A206840 A206841 A206842


KEYWORD

nonn,easy


AUTHOR

R. H. Hardin, Feb 13 2012


EXTENSIONS

a(0)=1 prepended by Alois P. Heinz, Oct 26 2016


STATUS

approved



