cp's OEIS Frontend

A214977 Number of terms in Lucas representations of 1,2,...,n.

%I A214977 #7 Dec 04 2016 19:46:30
%S A214977 1,2,3,4,6,8,9,11,13,15,16,18,20,22,24,27,30,31,33,35,37,39,42,45,47,
%T A214977 50,53,56,57,59,61,63,65,68,71,73,76,79,82,84,87,90,93,96,100,104,105,
%U A214977 107,109,111,113,116,119,121,124,127,130,132,135,138,141,144
%N A214977 Number of terms in Lucas representations of 1,2,...,n.
%C A214977 See the conjecture at A214979.
%H A214977 Clark Kimberling, <a href="/A214977/b214977.txt">Table of n, a(n) for n = 1..10000</a>
%e A214977 n..Lucas(n)..# terms...A214977(n)
%e A214977 1..1.........1.........1
%e A214977 2..2.........1.........2
%e A214977 3..3.........1.........3
%e A214977 4..4.........1.........4
%e A214977 5..4+1.......2.........6
%e A214977 6..4+2.......2.........8
%e A214977 7..7.........1.........9
%e A214977 8..7+1.......2.........11
%e A214977 9..7+2.......2.........13
%t A214977 z = 200; s = Reverse[Sort[Table[LucasL[n - 1], {n, 1, 70}]]]; t1 = Map[Length[Select[Reap[FoldList[(Sow[Quotient[#1, #2]]; Mod[#1, #2]) &, #, s]][[2,1]], # > 0 &]] &, Range[z]]; u[n_] := Sum[t1[[k]], {k, 1, n}]; u1 = Table[u[n], {n, 1, z}]
%t A214977 (* _Peter J. C. Moses_, Oct 18 2012 *)
%Y A214977 Cf. A214978, A214979, A214980, A214981, A000032.
%K A214977 nonn
%O A214977 1,2
%A A214977 _Clark Kimberling_, Oct 22 2012