A318303 a(0) = 0, a(n) = n + a(n-1) if n is odd, a(n) = -3*a(n/2) if n is even.

0, 1, -3, 0, 9, 14, 0, 7, -27, -18, -42, -31, 0, 13, -21, -6, 81, 98, 54, 73, 126, 147, 93, 116, 0, 25, -39, -12, 63, 92, 18, 49, -243, -210, -294, -259, -162, -125, -219, -180, -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

Offset: 0

Author

Altug Alkan, Aug 24 2018

Keywords

• sign
• look

Comments

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.

Links

• Altug Alkan, Table of n, a(n) for n = 0..32767
• Rémy Sigrist, Colored scatterplot of a(n) for n = 0..1000000 (where the color is function of A262304(n))
• Rémy Sigrist, Colored scatterplot of a(n) for n = 0..1000000 (where the color is function of floor(n / 2^(A070939(n) - 6)))
• Rémy Sigrist, A colored scatterplot of (A317825(n), abs(A318303(n))) for n = 1..2^20-1 (where the color is function of floor(n / 2^(A070939(n)-5)))
• Altug Alkan, A scatterplot of (A317825(n), A318303(n)+A317825(n)) for n = 1..2^17-1

Crossrefs

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

Programs

Mathematica

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

PARI

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