A318303 - OEIS

%I #29 Sep 01 2018 12:38:30

%S 0,1,-3,0,9,14,0,7,-27,-18,-42,-31,0,13,-21,-6,81,98,54,73,126,147,93,

%T 116,0,25,-39,-12,63,92,18,49,-243,-210,-294,-259,-162,-125,-219,-180,

%U -378,-337,-441,-398,-279,-234,-348,-301,0,49,-75,-24,117,170,36,91,-189,-132,-276,-217,-54,7,-147,-84,729,794,630

%N a(0) = 0, a(n) = n + a(n-1) if n is odd, a(n) = -3*a(n/2) if n is even.

%C Let g_k(0) = 0.  g_k(n) = n + g_k(n-1) if n is odd, g_k(n) = k*a(n/2) if n is even. A228451(n) is g_1(n), A298011(n) is g_2(n). This sequence is a(n) = g_k(n) where k = -3.

%H Altug Alkan, <a href="/A318303/b318303.txt">Table of n, a(n) for n = 0..32767</a>

%H Rémy Sigrist, <a href="/A318303/a318303.png">Colored scatterplot of a(n) for n = 0..1000000</a> (where the color is function of A262304(n))

%H Rémy Sigrist, <a href="/A318303/a318303_1.png">Colored scatterplot of a(n) for n = 0..1000000</a> (where the color is function of floor(n / 2^(A070939(n) - 6)))

%H Rémy Sigrist, <a href="/A318303/a318303_2.png">A colored scatterplot of (A317825(n), abs(A318303(n))) for n = 1..2^20-1 </a> (where the color is function of floor(n / 2^(A070939(n)-5)))

%H Altug Alkan, <a href="/A318303/a318303_3.png">A scatterplot of (A317825(n), A318303(n)+A317825(n)) for n = 1..2^17-1</a>

%t Nest[Append[#1, If[OddQ@ #2, #2 + #1[[-1]], -3 #1[[#2/2 + 1]] ]] & @@ {#, Length@ #} &, {0}, 66] (* _Michael De Vlieger_, Aug 25 2018 *)

%o (PARI) a(n)=if(n==0, 0, if(n%2, n+a(n-1), -3*a(n/2)));

%Y Cf. A070939, A228451, A262304, A298011, A305865, A317825, A318265.

%K sign,look

%O 0,3

%A _Altug Alkan_, Aug 24 2018