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A099041 Number of 3 X n 0-1 matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (10;0) and (10;1). 0
8, 24, 58, 128, 270, 556, 1130, 2280, 4582, 9188, 18402, 36832, 73694, 147420, 294874, 589784, 1179606, 2359252, 4718546, 9437136, 18874318, 37748684, 75497418, 150994888 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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 g.f. 2xy/((1-2x)(1-(2-x)y/(1-x))).

LINKS

Table of n, a(n) for n=1..24.

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

G.f.: 2*x*(2-x)^2/((1-2*x)*(1-x)^2).

a(n) = 9*2^n - 2*n - 8.

a(n) = 2 * (A054127(n+1) - 1).

PROG

(PARI) vector(50, n, 9*2^n - 2*n - 8) \\ Michel Marcus, Dec 01 2014

CROSSREFS

Cf. A054127.

Sequence in context: A011925 A256052 A159741 * A129959 A256533 A177719

Adjacent sequences:  A099038 A099039 A099040 * A099042 A099043 A099044

KEYWORD

nonn

AUTHOR

Sergey Kitaev (kitaev(AT)ms.uky.edu), Nov 13 2004

STATUS

approved

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Last modified February 17 16:09 EST 2018. Contains 299296 sequences. (Running on oeis4.)