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
Offset: 0
Keywords
Examples
For n=7, as n is 3(2)+1, a(n) = A000045(2+1) = 2.
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).
Programs
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Mathematica
LinearRecurrence[{0, 0, 1, 0, 0, 1}, {1,1,0,1,1,1}, 50] -
Python
a = lambda x:[1,1,0,1,1,1][x] if x<6 else a(x-3)+a(x-6)
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Racket
(define (a x) (cond [(< x 6) (list-ref (list 1 1 0 1 1 1) x)] [else (+ (a (- x 3)) (a (- x 6)))]))
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Sage
s=((x^5 + x + 1)/(-x^6 - x^3 + 1)).series(x, 23); s.coefficients(x, sparse=False)
Comments