

A100313


Number of 4 X n binary matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (10;0) and (01;1).


1



1, 16, 96, 400, 1408, 4480, 13312, 37632, 102400, 270336, 696320, 1757184, 4358144, 10649600, 25690112, 61276160, 144703488, 338690048, 786432000, 1812987904, 4152360960, 9453961216, 21407727616, 48234496000, 108179488768, 241591910400, 537407782912
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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 01 matrices in question is given by the g.f. 2xy/(12(x+yxy)).


LINKS

Table of n, a(n) for n=0..26.
S. Kitaev, On multiavoidance 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 (8, 24, 32, 16).


FORMULA

G.f.: 1 + 16*x*(1x)^2/(12*x)^4.
a(n) = (1/3) n*(n^2+9n+14) * 2^n for n>0.
a(n) = 16 * A055585(n1) for n>0.


PROG

(PARI) vector(50, n, n*(n^2+9*n+14) * 2^n / 3) \\ Michel Marcus, Dec 01 2014


CROSSREFS

Cf. A055585, A100312 (m=3).
Sequence in context: A241937 A014344 A239613 * A091079 A321851 A185789
Adjacent sequences: A100310 A100311 A100312 * A100314 A100315 A100316


KEYWORD

nonn,easy


AUTHOR

Sergey Kitaev, Nov 13 2004


EXTENSIONS

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


STATUS

approved



