A099944 - OEIS

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A099944

Number of 3 X n binary matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1) and (11;0).

76, 164, 340, 692, 1396, 2804, 5620, 11252, 22516, 45044, 90100, 180212, 360436, 720884, 1441780, 2883572, 5767156, 11534324, 23068660, 46137332, 92274676, 184549364, 369098740, 738197492, 1476394996, 2952790004, 5905580020

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OFFSET

3,1

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 (m+3)*2^(m+n-2)-2^n-2^(m+1)+4 for m>0 and n>2; for n=2 the number is (m+1)*2^m.

LINKS

Table of n, a(n) for n=3..29.

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 (3,-2).

FORMULA

a(n) = 11*2^n - 12.

From Chai Wah Wu, Jun 06 2016: (Start)

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

G.f.: 4*x^3*(19 - 16*x)/((1 - x)*(1 - 2*x)). (End)

MATHEMATICA

LinearRecurrence[{3, -2}, {76, 164}, 30] (* Harvey P. Dale, Oct 22 2017 *)

PROG