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A253607 First differences of A253580, when the tree is seen as flattened list.

%I A253607 #7 Dec 23 2024 14:53:44
%S A253607 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 A253607 -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 A253607 -1,2,2,2,2,2,2,2,1,-2,-2,-2,-2,-2,-2,-2,-1,2,2
%N A253607 First differences of A253580, when the tree is seen as flattened list.
%C A253607 a(n) != 0 and -2 <= a(n) <= +2.
%C A253607 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 A253607 a(A005563(n)) = 1; a(A028387(n)) = -1;
%C A253607 a(A061885(n)) > 0; a(A064801(n)) < 0.
%H A253607 Reinhard Zumkeller, <a href="/A253607/b253607.txt">Table of n, a(n) for n = 0..10000</a>
%H A253607 Éric Angelini, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2015-January/014247.html">More fractal trees - and erasures</a>, SeqFan list, Jan 04 2015.
%e A253607 .   n | A253580(n) | a(n) | erased | reappearing
%e A253607 .  ---+------------+------+--------+-------------
%e A253607 .   0 |    X    0  |   1  |      0 |
%e A253607 .   1 |    X    1  |  -1  |      1 |
%e A253607 .   2 |         0  |   2  |        |           0
%e A253607 .   3 |    X    2  |   1  |      2 |
%e A253607 .   4 |    X    3  |  -2  |      3 |
%e A253607 .   5 |         1  |  -1  |        |           1
%e A253607 .   6 |         0  |   2  |        |           0
%e A253607 .   7 |         2  |   2  |        |           2
%e A253607 .   8 |    X    4  |   1  |      4 |
%e A253607 .   9 |    X    5  |  -2  |      5 |
%e A253607 .  10 |         3  |  -2  |        |           3
%e A253607 .  11 |         1  |  -1  |        |           1
%e A253607 .  12 |         0  |   2  |        |           0
%e A253607 .  13 |         2  |   2  |        |           2
%e A253607 .  14 |         4  |   2  |        |           4
%e A253607 .  15 |    X    6  |   1  |      6 |
%e A253607 .  16 |    X    7  |  -2  |      7 |
%e A253607 .  17 |         5  |  -2  |        |           5
%e A253607 .  18 |         3  |  -2  |        |           3
%e A253607 .  19 |         1  |  -1  |        |           1
%e A253607 .  20 |         0  |   2  |        |           0
%e A253607 .  21 |         2  |   2  |        |           2
%e A253607 .  22 |         4  |   2  |        |           4
%e A253607 .  23 |         6  |   2  |        |           6
%e A253607 .  24 |    X    8  |   1  |      8 |
%e A253607 .  25 |    X    9  |  -2  |      9 |             .
%o A253607 (Haskell)
%o A253607 a253607 n = a253607_list !! n
%o A253607 a253607_list = zipWith (-) (tail a253580_list) a253580_list
%Y A253607 Cf. A253580, A005563, A028387, A061885, A064801.
%K A253607 sign
%O A253607 0,3
%A A253607 _Reinhard Zumkeller_, Jan 05 2015