OFFSET
0,2
COMMENTS
a(n) is the cardinality of set s(n), where s(0) = {0} and s(n+1) = s(n) union {(i+j+1)/2 : i,j in s(n)}. s(4) = {0, 1/2, 3/4, 7/8, 15/16, 1, 17/16, 9/8, 19/16, 5/4, 21/16, 11/8, 23/16, 3/2, 25/16, 13/8, 27/16, 7/4, 29/16, 15/8, 31/16, 2} has cardinality a(4) = 22.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6,-13,12,-4).
FORMULA
G.f.: -(x^3-5*x^2+4*x-1)/((2*x-1)^2*(x-1)^2).
MAPLE
a:= n-> (n-2)*2^(n-1)+n+2:
seq(a(n), n=0..35);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Apr 10 2021
STATUS
approved