OFFSET
1,2
COMMENTS
a(n) can also be interpreted as the number of ON cells at the n-th stage of the following automaton:
- At first stage, we have only one ON cell at position 1,
- An ON cell appears at position x+y if the cells at positions x and y are ON,
- An ON cell dies at position x+y if the cells at positions x and y are ON.
a(n) <= 2^(n-1) for any n>0.
LINKS
FORMULA
EXAMPLE
Z(1) = {1};
Z(2) = {1} (+) {2} = {1,2};
Z(3) = {1,2} (+) {2,3,4} = {1,3,4};
Z(4) = {1,3,4} (+) {2,4,5,6,7,8} = {1,2,3,5,6,7,8};
Hence: a(1) = 1, a(2) = 2, a(3) = 3 and a(4) = 7.
PROG
(Perl) See Links section.
(PARI) lista(nn) = {zprec = Set([1]); print1(#zprec, ", "); for (n=2, nn, zs = setbinop((x, y)->x+y, zprec); zn = setminus(setunion(zprec, zs), setintersect(zprec, zs)); print1(#zn, ", "); zprec = zn; ); } \\ Michel Marcus, Oct 20 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul Tek, Oct 17 2015
STATUS
approved