cp's OEIS Frontend

A356995 a(n) = b(n) - b(b(n)) - b(n - b(n)) for n >= 3, where b(n) = A356988(n).

%I A356995 #12 Oct 13 2022 12:53:57
%S A356995 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,
%T A356995 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,
%U A356995 3,4,5,6,7,8,7,6,5,4,3,2,1,0,0,0,0,0,0
%N A356995 a(n) = b(n) - b(b(n)) - b(n - b(n)) for n >= 3, where b(n) = A356988(n).
%C A356995 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).
%C A356995 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}.
%F A356995 a(n+1) - a(n) is in {1, 0, -1}.
%F A356995 For k >= 3, a(L(k) + j) = F(k-3) - j and a(L(k) - j) = F(k-3) - j for 0 <= j <= F(k-3), where F(k) = A000045(k), the k-th Fibonacci number and L(k) = A000032(k), the k-th Lucas number.
%e A356995 Sequence {a(n)} arranged as a sequence of strings of length 2*Fibonacci(k), k >= 1
%e A356995   0, 0;
%e A356995   0, 0;
%e A356995   1, 0, 0, 0;
%e A356995   1, 0, 0, 0, 0, 0;
%e A356995   1, 2, 1, 0, 0, 0, 0, 0, 0, 0;
%e A356995   1, 2, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
%e A356995   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;
%e A356995   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;
%e A356995   ...
%p A356995 # b(n) = A356988(n)
%p A356995 b := proc(n) option remember; if n = 1 then 1 else n - b(b(n - b(b(b(n-1))))) end if; end proc:
%p A356995 seq(b(n) - b(b(n)) - b(n - b(n)), n = 3..250);
%Y A356995 Cf. A000032, A000045, A356988, A356991 - A356999.
%K A356995 nonn,easy
%O A356995 3,16
%A A356995 _Peter Bala_, Sep 09 2022