OFFSET
3,16
COMMENTS
Starting at n = 7, the sequence consists of successive blocks of integers of the form 1, 2, 3, ..., F(k) - 1, F(k), F(k) - 1, ..., 3, 2, 1, where F(k), k >= 1, denotes the k-th Fibonacci number, followed by a string of zeros conjecturally of length 1 + 2*F(k+1).
The sequence has local peak values at abscissa values n = 7, 11, 18, ..., L(k), ..., where L(k) = A000032(k), the k-th Lucas number. The zero strings begin at abscissa values n = 8, 12, 20, 32, 52, ..., equal to the sequence {L(k) + F(k-3) : k >= 4} = {4*F(k-1): k >= 4}.
FORMULA
EXAMPLE
Sequence {a(n)} arranged as a sequence of strings of length 2*Fibonacci(k), k >= 1
0, 0;
0, 0;
1, 0, 0, 0;
1, 0, 0, 0, 0, 0;
1, 2, 1, 0, 0, 0, 0, 0, 0, 0;
1, 2, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
1, 2, 3, 4, 5, 4, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
1, 2, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
...
MAPLE
# b(n) = A356988(n)
b := proc(n) option remember; if n = 1 then 1 else n - b(b(n - b(b(b(n-1))))) end if; end proc:
seq(b(n) - b(b(n)) - b(n - b(n)), n = 3..250);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Peter Bala, Sep 09 2022
STATUS
approved