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A100312 Number of 3 X n binary matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (10;0) and (01;1). 1
1, 8, 32, 104, 304, 832, 2176, 5504, 13568, 32768, 77824, 182272, 421888, 966656, 2195456, 4947968, 11075584, 24641536, 54525952, 120061952, 263192576, 574619648, 1249902592, 2709520384, 5855248384, 12616466432, 27111981056, 58116276224, 124285616128 (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 the g.f. 2xy/(1-2(x+y-xy)).

LINKS

Table of n, a(n) for n=0..28.

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

FORMULA

G.f.: 1 + 8*x*(1-x)^2/(1-2*x)^3.

a(n) = (n^2 + 5n + 2) * 2^(n-1).

a(n) = 8 * A049611(n) for n>0.

PROG

(PARI) vector(50, n, (n^2 + 5*n + 2) * 2^(n-1)) \\ Michel Marcus, Dec 01 2014

CROSSREFS

Cf. A049611, A100313 (m=3).

Sequence in context: A195590 A071345 A178797 * A302507 A204643 A003201

Adjacent sequences:  A100309 A100310 A100311 * A100313 A100314 A100315

KEYWORD

nonn

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 15 15:14 EDT 2019. Contains 328030 sequences. (Running on oeis4.)