A099003 Number of 4 X n 0-1 matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (10;0) and (11;0).

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

Offset: 0

Author

Sergey Kitaev, Nov 13 2004

Keywords

• nonn
• easy

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 2^(m+n) - 2^m - 2^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) = 1 - c + c*2^(n-1) if the offset 1 is chosen. The o.g.f. of the a(n) is x*(1+(c-2)x)/((2x-1)*(x-1)). 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

• 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).

Crossrefs

Cf. A048489 (m=3).

Programs

Mathematica

LinearRecurrence[{3,-2},{1,16},40] (* Harvey P. Dale, May 20 2018 *)

Formula

a(n) = 15*2^n - 14.

O.g.f.: (1+13x)/((x-1)(2x-1)). - R. J. Mathar, May 06 2008