

A099003


Number of 4 X n 01 matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (10;0) and (11;0).


8



1, 16, 46, 106, 226, 466, 946, 1906, 3826, 7666, 15346, 30706, 61426, 122866, 245746, 491506, 983026, 1966066, 3932146, 7864306, 15728626, 31457266, 62914546, 125829106, 251658226, 503316466, 1006632946, 2013265906, 4026531826
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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+n)2^m2^n+2.
Binomial transform of 1,15,15,.. (15 infinitely repeated).  Gary W. Adamson, Apr 29 2008
The binomial transform of [1, c, c, c,...] has the terms a(n)=1c+c*2^(n1) if the offset 1 is chosen. The o.g.f. of the a(n) is x{1+(c2)x}/{(2x1)(x1)}. This applies to A139634 with c=10, to A139635 with c=11, to A139697 with c=12, to A139698 with c=25 and to A099003, A139700, A139701 accordingly.  R. J. Mathar, May 11 2008


LINKS

Table of n, a(n) for n=0..28.
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 (3,2).


FORMULA

a(n) = 15*2^n14.
O.g.f.: (1+13x)/((x1)(2x1)).  R. J. Mathar, May 06 2008


MATHEMATICA

a=1; lst={a}; k=15; Do[a+=k; AppendTo[lst, a]; k+=k, {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 17 2008 *)
LinearRecurrence[{3, 2}, {1, 16}, 40] (* Harvey P. Dale, May 20 2018 *)


CROSSREFS

Cf. A048489 (m=3).
Sequence in context: A235772 A235555 A069128 * A124709 A244094 A235549
Adjacent sequences: A099000 A099001 A099002 * A099004 A099005 A099006


KEYWORD

nonn,easy


AUTHOR

Sergey Kitaev, Nov 13 2004


STATUS

approved



