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A206839 Number of 1 X n 0..3 arrays avoiding the pattern z-2 z-1 z in any row, column, nw-to-se diagonal or ne-to-sw 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 (list; graph; refs; listen; history; text; internal format)
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(n-1) -2*a(n-3) +a(n-4).

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-> (<<0|1|0|0>, <0|0|1|0>, <0|0|0|1>, <1|-2|0|4>>^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

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Last modified December 8 07:30 EST 2022. Contains 358677 sequences. (Running on oeis4.)