|
%I #19 Apr 14 2021 05:23:16
%S 0,0,1,1,1,1,2,2,2,1,2,2,2,2,3,3,3,2,3,2,2,2,3,3,3,2,3,3,3,3,4,4,4,3,
%T 4,3,3,3,4,3,3,2,3,3,3,3,4,4,4,3,4,3,3,3,4,4,4,3,4,4,4,4,5,5,5,4,5,4,
%U 4,4,5,4,4,3,4,4,4,4,5,4,4,3,4,3,3,3,4,4,4,3
%N Number of i such that d(i) <= d(i-1), where Sum_{i=0..m} d(i)*2^i is the base-2 representation of n.
%H Ralf Stephan, <a href="/somedcgf.html">Some divide-and-conquer sequences ...</a>
%H Ralf Stephan, <a href="/A079944/a079944.ps">Table of generating functions</a>
%F From _Ralf Stephan_, Oct 05 2003: (Start)
%F G.f.: -1/(1-x) + 1/(1-x) * Sum_{k>=0} (t + t^3 + t^4)/(1 + t + t^2 + t^3), t=x^2^k).
%F a(n) = A056973(n) + A000120(n) - 1.
%F a(n) = b(n) - 1, with b(0)=0, b(2n) = b(n) + [n even], b(2n+1) = b(n) + 1. (End)
%e The base-2 representation of n=4 is 100 with d(0)=0, d(1)=0, d(2)=1. There is one fall-or-equal from d(0) to d(1), so a(4)=1. - _R. J. Mathar_, Oct 16 2015
%p A037809 := proc(n)
%p a := 0 ;
%p dgs := convert(n,base,2);
%p for i from 2 to nops(dgs) do
%p if op(i,dgs)<=op(i-1,dgs) then
%p a := a+1 ;
%p end if;
%p end do:
%p a ;
%p end proc: # _R. J. Mathar_, Oct 16 2015
%Y Cf. A033265.
%K nonn,base
%O 1,7
%A _Clark Kimberling_
%E Sign in Name corrected by _R. J. Mathar_, Oct 16 2015
|
