cp's OEIS Frontend

A245541 Write n>=1 as either n=2^k-2^r with 0 <= r <= k-1, in which case a(2^k-2^r)=(k-r)*(k-r+1)/2, or as n=2^k-2^r+j with 2 <= r <= k-1, 1 <= j < 2^r-1, in which case a(2^k-2^r+j)=((k-r)*(k-r+1)/2)*a(j).

%I A245541 #18 Jul 27 2014 12:22:23
%S A245541 1,1,3,1,1,3,6,1,1,1,3,3,3,6,10,1,1,1,3,1,1,3,6,3,3,3,9,6,6,10,15,1,1,
%T A245541 1,3,1,1,3,6,1,1,1,3,3,3,6,10,3,3,3,9,3,3,9,18,6,6,6,18,10,10,15,21,1,
%U A245541 1,1,3,1,1,3,6,1,1,1,3,3,3,6,10,1,1,1,3,1,1,3,6,3,3,3,9,6,6,10,15
%N A245541 Write n>=1 as either n=2^k-2^r with 0 <= r <= k-1, in which case a(2^k-2^r)=(k-r)*(k-r+1)/2, or as n=2^k-2^r+j with 2 <= r <= k-1, 1 <= j < 2^r-1, in which case a(2^k-2^r+j)=((k-r)*(k-r+1)/2)*a(j).
%C A245541 See A245196 for a list of other sequences produced by this type of recurrence.
%C A245541 It follows from the definition that the final entries in the blocks are triangular numbers.
%e A245541 Arranged into blocks:
%e A245541 1,
%e A245541 1, 3,
%e A245541 1, 1, 3, 6,
%e A245541 1, 1, 1, 3, 3, 3, 6, 10,
%e A245541 1, 1, 1, 3, 1, 1, 3, 6, 3, 3, 3, 9, 6, 6, 10, 15,
%e A245541 1, 1, 1, 3, 1, 1, 3, 6, 1, 1, 1, 3, 3, 3, 6, 10, 3, 3, 3, 9, 3, 3, 9, 18, 6, 6, 6, 18, 10, 10, 15, 21,
%e A245541 ...
%p A245541 G:=[seq(n,n=0..30)];
%p A245541 m:=1;
%p A245541 f:=proc(n) option remember; global m,G; local k,r,j,np;
%p A245541    k:=1+floor(log[2](n)); np:=2^k-n;
%p A245541    if np=1 then r:=0; j:=0; else r:=1+floor(log[2](np-1)); j:=2^r-np; fi;
%p A245541    if j=0 then G[k-r]; else m*G[k-r]*f(j); fi;
%p A245541 end;
%p A245541 [seq(f(n),n=1..120)];
%Y A245541 Cf. A245196, A245547.
%K A245541 nonn,tabf
%O A245541 1,3
%A A245541 _N. J. A. Sloane_, Jul 26 2014