A099945 Number of 4 X n binary matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1) and (11;0).

188, 404, 836, 1700, 3428, 6884, 13796, 27620, 55268, 110564, 221156, 442340, 884708, 1769444, 3538916, 7077860, 14155748, 28311524, 56623076, 113246180, 226492388, 452984804, 905969636, 1811939300, 3623878628, 7247757284

Offset

3,1

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 (m+3)*2^(m+n-2)-2^n-2^(m+1)+4 for m>0 and n>2; for n=2 the number is (m+1)*2^m.

Links

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

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 (3, -2).

Formula

a(n) = 27*2^n-28.

Prog

(PARI) vector(50, n, i=n+2; 27*2^i-28) \\ Michel Marcus, Dec 01 2014

Crossrefs

Cf. A000105.

Sequence in context: A186397 A260836 A304279 * A211814 A335592 A233786

Adjacent sequences: A099942 A099943 A099944 * A099946 A099947 A099948

Keyword

nonn

Author

Sergey Kitaev, Nov 12 2004

Status

approved