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
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
KEYWORD
nonn,easy
AUTHOR
Sergey Kitaev, Nov 13 2004
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Dec 21 2018
STATUS
approved