A356388 - OEIS

%I #8 Aug 07 2022 15:36:56

%S 1,-1,-3,-3,3,-16,-16,-8,-8,8,24,24,-24,-210,-210,-105,-105,105,-42,

%T -42,-21,-21,21,63,63,-63,336,336,168,168,-168,-504,-504,504,-7150,

%U -7150,-3575,-3575,3575,-1430,-1430,-715,-715,715,2145,2145,-2145,-550,-550

%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 A356387 for similar sequences.

%H Rémy Sigrist, <a href="/A356388/b356388.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(-4) + F(-6),

%e - so a(11) = F(-4) * F(-6) = -3 * -8 = 24.

%o (PARI) a(n) = { my (v=1); n=-n; 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, A215023, A273156, A356387.

%K sign,base

%O 0,3

%A _Rémy Sigrist_, Aug 05 2022