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A067150
Number of integers i=1,2,...,n such that (n,i) has Property F3*, i.e., i and n are consecutive terms of a sequence b(k) satisfying b(1)=1, b(n) = (b(n-1) OR 2*b(n-1)) + b(n-2), where the OR is taken bitwise.
1
0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 2, 3, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 2, 1, 1, 1, 0, 1, 2, 0, 3, 5, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0
OFFSET
1,16
COMMENTS
Surprisingly, for k > 0, we find that a(2^k) = F(k-1), where {F(n)} is the sequence of Fibonacci numbers (A000045). Also, except for n = 2^3 = 8, these values are exactly those where new records in a(n) are made.
The definition can be restated as follows: a(n) is the number of integers i, 0 < i < n such that i and n are consecutive terms of some sequence b(k) satisfying b(1)=1 and b(k) = 3#b(k-1) + b(k-2), where # denotes OR-numbral multiplication (see A048888 for the definition).
If the OR-numbral multiplier 3 in the definition is replaced by 7, the resulting sequence has as record values the tribonacci numbers in A000073.
LINKS
A. Frosini and S. Rinaldi, On the Sequence A079500 and Its Combinatorial Interpretations, J. Integer Seq., Vol. 9 (2006), Article 06.3.1.
CROSSREFS
KEYWORD
nonn
AUTHOR
John W. Layman, Jan 05 2002
STATUS
approved