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A100316 Number of 4 X n 0-1 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 (list; graph; refs; listen; history; text; internal format)
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 2^m+2^n+2(nm-n-m).

LINKS

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

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

a(n) = 2^n + 6*n + 8 for n>0, a(0) = 1.

G.f.: -(16*x^3-35*x^2+12*x+1)/((2*x-1)*(x-1)^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

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Last modified February 20 00:28 EST 2019. Contains 320329 sequences. (Running on oeis4.)