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%I #6 Jan 02 2023 12:30:51
%S 1,-1,2,1,-2,-1,2,2,1,-2,-2,-1,2,2,2,1,-2,-2,-2,-1,2,2,2,2,1,-2,-2,-2,
%T -2,-1,2,2,2,2,2,1,-2,-2,-2,-2,-2,-1,2,2,2,2,2,2,1,-2,-2,-2,-2,-2,-2,
%U -1,2,2,2,2,2,2,2,1,-2,-2,-2,-2,-2,-2,-2,-1,2,2
%N First differences of A253580, when the tree is seen as flattened list.
%C a(n) != 0 and -2 <= a(n) <= +2.
%C a(n) = 1 iff A253580(n+1) = A253580(n) + 1, marked with X in the table below, where also the erasure of pairs of consecutive terms in A253580 is illustrated;
%C a(A005563(n)) = 1; a(A028387(n)) = -1;
%C a(A061885(n)) > 0; a(A064801(n)) < 0.
%H Reinhard Zumkeller, <a href="/A253607/b253607.txt">Table of n, a(n) for n = 0..10000</a>
%H Éric Angelini, <a href="http://list.seqfan.eu/oldermail/seqfan/2015-January/014247.html">More fractal trees - and erasures</a>, SeqFan list, Jan 04 2015.
%e . n | A253580(n) | a(n) | erased | reappearing
%e . ---+------------+------+--------+-------------
%e . 0 | X 0 | 1 | 0 |
%e . 1 | X 1 | -1 | 1 |
%e . 2 | 0 | 2 | | 0
%e . 3 | X 2 | 1 | 2 |
%e . 4 | X 3 | -2 | 3 |
%e . 5 | 1 | -1 | | 1
%e . 6 | 0 | 2 | | 0
%e . 7 | 2 | 2 | | 2
%e . 8 | X 4 | 1 | 4 |
%e . 9 | X 5 | -2 | 5 |
%e . 10 | 3 | -2 | | 3
%e . 11 | 1 | -1 | | 1
%e . 12 | 0 | 2 | | 0
%e . 13 | 2 | 2 | | 2
%e . 14 | 4 | 2 | | 4
%e . 15 | X 6 | 1 | 6 |
%e . 16 | X 7 | -2 | 7 |
%e . 17 | 5 | -2 | | 5
%e . 18 | 3 | -2 | | 3
%e . 19 | 1 | -1 | | 1
%e . 20 | 0 | 2 | | 0
%e . 21 | 2 | 2 | | 2
%e . 22 | 4 | 2 | | 4
%e . 23 | 6 | 2 | | 6
%e . 24 | X 8 | 1 | 8 |
%e . 25 | X 9 | -2 | 9 | .
%o (Haskell)
%o a253607 n = a253607_list !! n
%o a253607_list = zipWith (-) (tail a253580_list) a253580_list
%Y Cf. A253580, A005563, A028387, A061885, A064801.
%K sign
%O 0,3
%A _Reinhard Zumkeller_, Jan 05 2015
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