A227355 Product of run lengths in Zeckendorf representation of n.

1, 1, 1, 2, 1, 3, 2, 1, 4, 3, 2, 2, 1, 5, 4, 3, 4, 2, 3, 2, 1, 6, 5, 4, 6, 3, 6, 4, 2, 4, 3, 2, 2, 1, 7, 6, 5, 8, 4, 9, 6, 3, 8, 6, 4, 4, 2, 5, 4, 3, 4, 2, 3, 2, 1, 8, 7, 6, 10, 5, 12, 8, 4, 12, 9, 6, 6, 3, 10, 8, 6, 8, 4, 6, 4, 2, 6, 5, 4, 6, 3, 6, 4, 2, 4, 3

Offset

0,4

Comments

The same sequence also gives the product for the lengths of zero-runs only, as by definition, no two consecutive 1's can occur in Fibonacci number system (aka Zeckendorf representation), thus any 1's present contribute just *1 to the total product.

Links

Antti Karttunen, Table of n, a(n) for n = 0..10946

Formula

a(n) = A167489(A003714(n)) = A227350(A003714(n)).

a(A227352(A005408(n))) = A167489(n).

For n>= 3, a(A000045(n)) = n-2.

Prog

(Scheme) (define (A227355 n) (A167489 (A003714 n)))(define (A227355v2 n) (A227350 (A003714 n))) ;; Alternative definition.

Crossrefs

Cf. A167489, A003714, A102364, A014417, A227350.

Sequence in context: A049085 A193173 A331581 * A226080 A167287 A007336

Adjacent sequences: A227352 A227353 A227354 * A227356 A227357 A227358

Keyword

nonn,base

Author

Antti Karttunen, Jul 08 2013

Status

approved