A245565 - OEIS

%I #16 Sep 08 2014 10:39:58

%S 1,2,2,5,2,4,5,12,2,4,4,10,5,10,12,29,2,4,4,10,4,8,10,24,5,10,10,25,

%T 12,24,29,70,2,4,4,10,4,8,10,24,4,8,8,20,10,20,24,58,5,10,10,25,10,20,

%U 25,60,12,24,24,60,29,58,70,169,2,4,4,10,4,8,10,24,4,8,8,20,10,20,24,58,4,8,8,20,8,16

%N a(n) = Product_{i in row n of A245562} Pell(i+1).

%C This is the Run Length Transform of S(n) = Pell(n+1) (cf. A000129).

%C 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).

%H Alois P. Heinz, <a href="/A245565/b245565.txt">Table of n, a(n) for n = 0..8191</a>

%p A000129 := proc(n) option remember; if n <=1 then n; else 2*A000129(n-1)+A000129(n-2); fi; end;

%p ans:=[];

%p for n from 0 to 100 do lis:=[]; t1:=convert(n,base,2); L1:=nops(t1);

%p out1:=1; c:=0;

%p for i from 1 to L1 do

%p    if out1 = 1 and t1[i] = 1 then out1:=0; c:=c+1;

%p    elif out1 = 0 and t1[i] = 1 then c:=c+1;

%p    elif out1 = 1 and t1[i] = 0 then c:=c;

%p    elif out1 = 0 and t1[i] = 0 then lis:=[c,op(lis)]; out1:=1; c:=0;

%p    fi;

%p    if i = L1 and c>0 then lis:=[c,op(lis)]; fi;

%p                    od:

%p a:=mul(A000129(i+1), i in lis);

%p ans:=[op(ans),a];

%p od:

%p ans;

%Y Cf. A245562, A000129, A001045, A071053, A245564.

%K nonn,base

%O 0,2

%A _N. J. A. Sloane_, Aug 10 2014; revised Sep 05 2014