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A100315 Number of 3 X n 0-1 matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01;0), (10;0) and (01;1). 3
1, 8, 14, 22, 34, 54, 90, 158, 290, 550, 1066, 2094, 4146, 8246, 16442, 32830, 65602, 131142, 262218, 524366, 1048658, 2097238, 4194394, 8388702, 16777314, 33554534, 67108970, 134217838, 268435570, 536871030, 1073741946, 2147483774, 4294967426, 8589934726 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

An occurrence of a ranpp (xy;z) in a matrix A=(a(i,j)) is a triple (a(i1,j1), a(i1,j2), a(i2,j1)) where i1<i2, j1<j2 and these elements are in the same relative order as those in the triple (x,y,z). In general, the number of m X n 0-1 matrices in question is given by 2^m+2^n+2(nm-n-m).

LINKS

Table of n, a(n) for n=0..33.

S. Kitaev, On multi-avoidance of right angled numbered polyomino patterns, Integers: Electronic Journal of Combinatorial Number Theory 4 (2004), A21, 20pp.

Index entries for linear recurrences with constant coefficients, signature (4, -5, 2).

FORMULA

a(n) = 2^n+4*n+2 for n>0, a(0)=1.

From Chai Wah Wu, Aug 26 2016: (Start)

a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3) for n > 3.

G.f.: 1 + 2*x*(4 - 9*x + 3*x^2)/((1 - x )^2*(1 - 2*x)). (End)

MATHEMATICA

Table[4*n + 2^n + 2, {n, 50}] (* Vladimir Joseph Stephan Orlovsky, Jul 08 2011 *)

CROSSREFS

Cf. A100314 (m=2), A100316 (m=4).

Sequence in context: A287177 A063216 A238290 * A224952 A248700 A001049

Adjacent sequences:  A100312 A100313 A100314 * A100316 A100317 A100318

KEYWORD

nonn,easy

AUTHOR

Sergey Kitaev, Nov 13 2004

EXTENSIONS

a(0)=1 prepended by Alois P. Heinz, Dec 21 2018

STATUS

approved

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Last modified October 17 22:28 EDT 2019. Contains 328134 sequences. (Running on oeis4.)