|
|
A100314
|
|
Number of 2 X n 0-1 matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01;0), (10;0) and (01;1).
|
|
11
|
|
|
1, 4, 8, 14, 24, 42, 76, 142, 272, 530, 1044, 2070, 4120, 8218, 16412, 32798, 65568, 131106, 262180, 524326, 1048616, 2097194, 4194348, 8388654, 16777264, 33554482, 67108916, 134217782, 268435512, 536870970, 1073741884, 2147483710, 4294967360, 8589934658
(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*(n*m-n-m).
|
|
REFERENCES
|
Arthur H. Stroud, Approximate calculation of multiple integrals, Prentice-Hall, 1971.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 2^n + 2*n.
Binomial transform of (1, 3, 1, 1, 1, ...).
For n > 0, a(n) = 2*A005126(n-1). (End)
G.f.: 1 + 2*x*(2 -4*x +x^2)/((1-x)^2*(1-2*x)).
a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3).
G.f.: (1 - 3*x^2)/((1-x)^2*(1-2*x)). (End)
|
|
MAPLE
|
a:= proc(n) 2^n + 2*n: end: seq(a(n), n=0..50); # Gary W. Adamson, Jul 20 2007
|
|
MATHEMATICA
|
|
|
PROG
|
(SageMath) [2^n +2*n for n in range(41)] # G. C. Greubel, Feb 01 2023
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|