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).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Sergey 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.: (1+12*x-35*x^2+16*x^3)/((1-2*x)*(1-x)^2). - Alois P. Heinz, Dec 21 2018
E.g.f.: exp(2*x) + 2*(4+3*x)*exp(x) - 8. - G. C. Greubel, Feb 01 2023
MATHEMATICA
Table[If[n==0, 1, 2^n+6*n+8], {n, 0, 50}] (* Vladimir Joseph Stephan Orlovsky, Jul 08 2011 *)
PROG
(Magma) [2^n+6*n+8*(1-0^n): n in [0..40]]; // G. C. Greubel, Feb 01 2023
(SageMath) [2^n+6*n+8*(1-0^n) for n in range(41)] # G. C. Greubel, Feb 01 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Sergey Kitaev, Nov 13 2004
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Dec 21 2018
STATUS
approved