A356387 a(n) is the product of all parts in negaFibonacci representation of n.

1, 1, 2, 2, -5, 5, 5, 10, 10, 39, -39, -39, -13, 13, 13, 26, 26, -65, 65, 65, 130, 130, -816, 816, 816, 272, -272, -272, -544, -544, 102, -102, -102, -34, 34, 34, 68, 68, -170, 170, 170, 340, 340, 1326, -1326, -1326, -442, 442, 442, 884, 884, -2210, 2210, 2210

Offset: 0

Author

Rémy Sigrist, Aug 05 2022

Keywords

• sign
• base

Comments

a(0) = 1 for the empty product.

See A273156 and A356388 for similar sequences.

Examples

			For n = 11:
- using F(-k) = A039834(k):
- 11 = F(-1) + F(-4) + F(-7),
- so a(11) = F(-1) * F(-4) * F(-7) = 1 * -3 * 13 = -39.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10946
• Wikipedia, NegaFibonacci coding
• Index entries for sequences related to Zeckendorf expansion of n

Crossrefs

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

Programs

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) }