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A318488 a(0) = 0, a(n) = -5*a(n/3) if n is divisible by 3, otherwise a(n) = n + a(n-1).

%I A318488 #24 Sep 08 2022 08:46:22
%S A318488 0,1,3,-5,-1,4,-15,-8,0,25,35,46,5,18,32,-20,-4,13,75,94,114,40,62,85,
%T A318488 0,25,51,-125,-97,-68,-175,-144,-112,-230,-196,-161,-25,12,50,-90,-50,
%U A318488 -9,-160,-117,-73,100,146,193,20,69,119,-65,-13,40,-375,-320,-264,-470,-412,-353,-570,-509,-447,-200,-136,-71,-310
%N A318488 a(0) = 0, a(n) = -5*a(n/3) if n is divisible by 3, otherwise a(n) = n + a(n-1).
%C A318488 From a generalization of A318303 (compare the scatterplots in order to observe connection). In this case, A000244 is determinative for the boundaries of self-similar block structures of this sequence, i.e., n = 3^9 - 1 is a corresponding endpoint.
%H A318488 Altug Alkan, <a href="/A318488/b318488.txt">Table of n, a(n) for n = 0..19682</a>
%H A318488 Rémy Sigrist, <a href="/A318488/a318488.png">Colored scatterplot of a(n) for n = 0..3^10-1</a> (where the color is function of floor(n / 3^(A081604(n)-5)))
%t A318488 a[0]=0; a[n_] := a[n] = If[Mod[n, 3] == 0, -5 a[n/3], n + a[n - 1]]; Array[a, 70, 0] (* _Giovanni Resta_, Aug 27 2018 *)
%o A318488 (PARI) a(n)=if(n==0, 0, if(n%3, n+a(n-1), -5*a(n/3)));
%o A318488 (Magma) [0] cat [n eq 1 select 1 else n mod 3 eq 0 select -5*Self(n div 3) else Self(n-1)+n: n in [1..70]]; // _Vincenzo Librandi_, Aug 28 2018
%Y A318488 Cf. A081604, A318303.
%K A318488 sign,look
%O A318488 0,3
%A A318488 _Altug Alkan_, Aug 27 2018