cp's OEIS Frontend

A347060 Total number of 1's in the binary expansion of parts in all partitions of n into distinct parts.

%I A347060 #15 Aug 15 2021 18:14:56
%S A347060 0,1,1,4,4,7,11,15,20,28,39,48,64,80,104,134,167,203,257,311,381,470,
%T A347060 566,680,820,981,1168,1394,1650,1946,2300,2700,3161,3705,4315,5026,
%U A347060 5845,6769,7827,9049,10424,11992,13784,15801,18088,20702,23620,26922,30665
%N A347060 Total number of 1's in the binary expansion of parts in all partitions of n into distinct parts.
%H A347060 Alois P. Heinz, <a href="/A347060/b347060.txt">Table of n, a(n) for n = 0..10000</a>
%e A347060 a(5) = 7 counts the 1's in [101], [100, 1], [11, 10].
%p A347060 h:= proc(n) option remember; add(i, i=Bits[Split](n)) end:
%p A347060 b:= proc(n, i) option remember; `if`(n=0, [1, 0],
%p A347060       `if`(n>i*(i+1)/2, 0, b(n, i-1)+(p-> p+
%p A347060        [0, p[1]*h(i)])(b(n-i, min(n-i, i-1)))))
%p A347060     end:
%p A347060 a:= n-> b(n$2)[2]:
%p A347060 seq(a(n), n=0..60);
%Y A347060 Cf. A000009, A000120, A066189, A066624, A318756, A319140.
%K A347060 nonn,base
%O A347060 0,4
%A A347060 _Alois P. Heinz_, Aug 14 2021