cp's OEIS Frontend

A356996 a(n) = b(n) - b(b(n)) - b(n - b(n)) for n >= 3, where b(n) = A356989(n).

%I A356996 #15 May 13 2023 08:26:42
%S A356996 0,0,0,0,0,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,1,2,1,0,0,0,0,0,0,0,0,1,2,
%T A356996 3,2,1,0,0,0,0,0,0,0,0,0,0,0,1,2,3,4,3,2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A356996 0,0,0,1,2,3,4,5,6,5,4,3,2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,4,5,6,7,8,9,8,7,6,5,4,3,2,1,0
%N A356996 a(n) = b(n) - b(b(n)) - b(n - b(n)) for n >= 3, where b(n) = A356989(n).
%C A356996 The sequence appears to consist of blocks of terms of the form 1, 2, 3, ..., A(k) - 1, A(k), A(k) - 1, ..., 3, 2, 1, where A(k) = A000930(k), separated by blocks of consecutive zeros.
%C A356996 The sequence of local peak values of the line graph of the sequence {a(n)} begins 1, 1, 1, 2, 3, 4, 6, 9, 13, 19, ..., conjecturally A000930; the local peaks occur at abscissa values n = 8, 12, 17, 25, 37, 54, 79, 116, 170, 249, ..., conjecturally {A179070(k): k >= 7}. Cf. A356995 and A356997.
%F A356996 a(n+1) - a(n) belongs to {1, 0, -1}.
%e A356996 Sequence arranged as an irregular triangle; after the first row of zeros the row lengths are conjecturally equal to A164316(k) for k >= 2.
%e A356996 0, 0, 0, 0, 0;
%e A356996 1, 0, 0, 0;
%e A356996 1, 0, 0, 0, 0;
%e A356996 1, 0, 0, 0, 0, 0, 0;
%e A356996 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0;
%e A356996 1, 2, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
%e A356996 1, 2, 3, 4, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
%e A356996 1, 2, 3, 4, 5, 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;
%e A356996 ...
%p A356996 # b(n) = A356989
%p A356996 b := proc(n) option remember; if n = 1 then 1 else n - b(b(b(n - b(b(b(b(n-1))))))) end if; end proc:
%p A356996 seq(b(n) - b(b(n)) - b(n - b(n)), n = 3..300);
%Y A356996 Cf. A000930, A164316, A179070, A356989, A356995, A356997.
%K A356996 nonn,easy
%O A356996 3,23
%A A356996 _Peter Bala_, Sep 10 2022