

A246011


a(n) = Product_{i in row n of A245562} Lucas(i+1), where Lucas = A000204.


1



1, 3, 3, 4, 3, 9, 4, 7, 3, 9, 9, 12, 4, 12, 7, 11, 3, 9, 9, 12, 9, 27, 12, 21, 4, 12, 12, 16, 7, 21, 11, 18, 3, 9, 9, 12, 9, 27, 12, 21, 9, 27, 27, 36, 12, 36, 21, 33, 4, 12, 12, 16, 12, 36, 16, 28, 7, 21, 21, 28, 11, 33, 18, 29, 3, 9, 9, 12, 9, 27, 12, 21, 9, 27, 27, 36, 12, 36, 21, 33, 9, 27, 27, 36, 27
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OFFSET

0,2


COMMENTS

This is the Run Length Transform of S(n) = Lucas(n+1) = 1,3,4,7,11,... (cf. A000204).
The Run Length Transform of a sequence {S(n), n>=0} is defined to be the sequence {T(n), n>=0} given by T(n) = Product_i S(i), where i runs through the lengths of runs of 1's in the binary expansion of n. E.g. 19 is 10011 in binary, which has two runs of 1's, of lengths 1 and 2. So T(19) = S(1)*S(2). T(0)=1 (the empty product).


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..8191


EXAMPLE

From Omar E. Pol, Feb 15 2015: (Start)
Written as an irregular triangle in which row lengths are the terms of A011782:
1;
3;
3,4;
3,9,4,7;
3,9,9,12,4,12,7,11;
3,9,9,12,9,27,12,21,4,12,12,16,7,21,11,18;
3,9,9,12,9,27,12,21,9,27,27,36,12,36,21,33,4,12,12,16,12,36,16,28,7,21,21,28,11,33,18,29;
...
Right border gives the Lucas numbers (beginning with 1). This is simply a restatement of the theorem that this sequence is the Run Length Transform of A000204.
(End)


MAPLE

A000204 := proc(n) option remember; if n <=2 then 2*n1; else A000204(n1)+A000204(n2); fi; end;
ans:=[];
for n from 0 to 100 do lis:=[]; t1:=convert(n, base, 2); L1:=nops(t1);
out1:=1; c:=0;
for i from 1 to L1 do
if out1 = 1 and t1[i] = 1 then out1:=0; c:=c+1;
elif out1 = 0 and t1[i] = 1 then c:=c+1;
elif out1 = 1 and t1[i] = 0 then c:=c;
elif out1 = 0 and t1[i] = 0 then lis:=[c, op(lis)]; out1:=1; c:=0;
fi;
if i = L1 and c>0 then lis:=[c, op(lis)]; fi;
od:
a:=mul(A000204(i+1), i in lis);
ans:=[op(ans), a];
od:
ans;


CROSSREFS

Cf. A245562A245565, A000204, A001045, A071053.
Sequence in context: A027011 A267048 A326401 * A061023 A057690 A318706
Adjacent sequences: A246008 A246009 A246010 * A246012 A246013 A246014


KEYWORD

nonn,base


AUTHOR

N. J. A. Sloane, Aug 10 2014; revised Sep 05 2014


STATUS

approved



