A245565 a(n) = Product_{i in row n of A245562} Pell(i+1).

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, 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, 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

Offset: 0

Author

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

Keywords

• nonn
• base

Comments

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

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

Crossrefs

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

Programs

Maple

A000129 := proc(n) option remember; if n <=1 then n; else 2*A000129(n-1)+A000129(n-2); 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(A000129(i+1), i in lis);
ans:=[op(ans),a];
od:
ans;