cp's OEIS Frontend

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.

%I A067150 #8 Jan 28 2019 10:00:42
%S A067150 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,
%T A067150 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,
%U A067150 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
%N 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.
%C A067150 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.
%C A067150 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).
%C A067150 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.
%H A067150 A. Frosini and S. Rinaldi, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL9/Frosini/fros2.html">On the Sequence A079500 and Its Combinatorial Interpretations</a>, J. Integer Seq., Vol. 9 (2006), Article 06.3.1.
%Y A067150 Cf. A000045, A000073, A067148.
%K A067150 nonn
%O A067150 1,16
%A A067150 _John W. Layman_, Jan 05 2002