A327035 - OEIS

A327035

An unbounded sequence consisting solely of Fibonacci numbers with the property that for any four consecutive terms the maximum term is the sum of the two minimum terms.

1, 1, 0, 1, 1, 1, 2, 2, 1, 3, 3, 2, 5, 5, 3, 8, 8, 5, 13, 13, 8, 21, 21, 13, 34, 34, 21, 55, 55, 34, 89, 89, 55, 144, 144, 89, 233, 233, 144, 377, 377, 233, 610, 610, 377, 987, 987, 610, 1597, 1597, 987, 2584, 2584, 1597, 4181, 4181, 2584, 6765, 6765, 4181

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,7

COMMENTS

This sequence was constructed to show that there are many sequences, besides those merging with multiples of the Padovan sequence A000931, with the property that for any four consecutive terms the maximum term is the sum of the two minimum terms. This refutes a conjecture that was formerly in that entry.

LINKS

Michael De Vlieger, Table of n, a(n) for n = 0..10000

David Nacin, Van der Laan Sequences and a Conjecture on Padovan Numbers, J. Int. Seq., Vol. 26 (2023), Article 23.1.2.

Index entries for linear recurrences with constant coefficients, signature (0, 0, 1, 0, 0, 1).

FORMULA

G.f.: (x^5 + x + 1)/(-x^6 - x^3 + 1).

a(3*n) = A000045(n+1), a(3*n+1) = A000045(n+1), a(3*n+2) = A000045(n).

a(n) = a(n-3) + a(n-6).

EXAMPLE

For n=7, as n is 3(2)+1, a(n) = A000045(2+1) = 2.

MATHEMATICA

LinearRecurrence[{0, 0, 1, 0, 0, 1}, {1, 1, 0, 1, 1, 1}, 50]