A356387 - OEIS

%I #9 Aug 07 2022 15:36:51

%S 1,1,2,2,-5,5,5,10,10,39,-39,-39,-13,13,13,26,26,-65,65,65,130,130,

%T -816,816,816,272,-272,-272,-544,-544,102,-102,-102,-34,34,34,68,68,

%U -170,170,170,340,340,1326,-1326,-1326,-442,442,442,884,884,-2210,2210,2210

%N a(n) is the product of all parts in negaFibonacci representation of n.

%C a(0) = 1 for the empty product.

%C See A273156 and A356388 for similar sequences.

%H Rémy Sigrist, <a href="/A356387/b356387.txt">Table of n, a(n) for n = 0..10946</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/NegaFibonacci_coding">NegaFibonacci coding</a>

%H <a href="/index/Z#Zeckendorf">Index entries for sequences related to Zeckendorf expansion of n</a>

%e For n = 11:

%e - using F(-k) = A039834(k):

%e - 11 = F(-1) + F(-4) + F(-7),

%e - so a(11) = F(-1) * F(-4) * F(-7) = 1 * -3 * 13 = -39.

%o (PARI) a(n) = { my (v=1); while (n, my (neg=0, pos=0, f); for (e=0, oo, f=fibonacci(-1-e); if (f<0, neg+=f, pos+=f); if (neg <=n && n <= pos, v*=f; n-=f; break))); return (v) }

%Y Cf. A039834, A059867, A215022, A273156, A356388.

%K sign,base

%O 0,3

%A _Rémy Sigrist_, Aug 05 2022