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).

1, 8, 24, 58, 128, 270, 556, 1130, 2280, 4582, 9188, 18402, 36832, 73694, 147420, 294874, 589784, 1179606, 2359252, 4718546, 9437136, 18874318, 37748684, 75497418, 150994888, 301989830, 603979716, 1207959490, 2415919040, 4831838142, 9663676348, 19327352762

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

Links

Table of n, a(n) for n=0..31.

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.: 1 + 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) for n>0.

Prog

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

Crossrefs

Cf. A054127.

Sequence in context: A256052 A159741 A302489 * A306056 A129959 A256533

Adjacent sequences: A099038 A099039 A099040 * A099042 A099043 A099044

Keyword

nonn,easy

Author

Sergey Kitaev, Nov 13 2004

Extensions

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

Status

approved