

A100316


Number of 4 X n 01 matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01;0), (10;0) and (01;1).


2



1, 16, 24, 34, 48, 70, 108, 178, 312, 574, 1092, 2122, 4176, 8278, 16476, 32866, 65640, 131182, 262260, 524410, 1048704, 2097286, 4194444, 8388754, 16777368, 33554590, 67109028, 134217898, 268435632, 536871094, 1073742012, 2147483842, 4294967496, 8589934798
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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 2^m+2^n+2(nmnm).


LINKS

Table of n, a(n) for n=0..33.
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 (4, 5, 2).


FORMULA

a(n) = 2^n + 6*n + 8 for n>0, a(0) = 1.
G.f.: (16*x^335*x^2+12*x+1)/((2*x1)*(x1)^2).  Alois P. Heinz, Dec 21 2018


MATHEMATICA

Table[6*n + 2^n + 8, {n, 50}] (* Vladimir Joseph Stephan Orlovsky, Jul 08 2011 *)


CROSSREFS

Cf. A100314 (m=2), A100315 (m=3).
Sequence in context: A082803 A273801 A163284 * A206260 A036328 A067028
Adjacent sequences: A100313 A100314 A100315 * A100317 A100318 A100319


KEYWORD

nonn


AUTHOR

Sergey Kitaev, Nov 13 2004


EXTENSIONS

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


STATUS

approved



