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
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.
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Programs
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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) }
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