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A319142 Total number of binary digits in the partitions of n into odd parts.

%I A319142 #15 Dec 12 2020 14:17:38
%S A319142 1,2,5,7,12,19,26,36,52,71,92,124,158,204,265,331,413,522,641,791,976,
%T A319142 1184,1435,1741,2093,2506,3005,3574,4237,5030,5928,6971,8202,9593,
%U A319142 11212,13087,15210,17653,20472,23665,27308,31488,36205,41570,47701,54584,62387
%N A319142 Total number of binary digits in the partitions of n into odd parts.
%H A319142 Alois P. Heinz, <a href="/A319142/b319142.txt">Table of n, a(n) for n = 1..10000</a>
%p A319142 h:= proc(n) option remember; 1+ilog2(n) end:
%p A319142 b:= proc(n, i) option remember; `if`(n=0, [1, 0],
%p A319142       `if`(i<1, 0, b(n, i-1-irem(i, 2))+`if`(i::even
%p A319142        or i>n, 0, (p-> p+[0, p[1]*h(i)])(b(n-i, i)))))
%p A319142     end:
%p A319142 a:= n-> b(n$2)[2]:
%p A319142 seq(a(n), n=1..60);  # _Alois P. Heinz_, Sep 27 2018
%t A319142 h[n_] := h[n] = 1 + Floor@Log[2, n];
%t A319142 b[n_, i_] := b[n, i] = If[n==0, {1, 0}, If[i<1, 0, b[n, i-1-Mod[i, 2]] + If[EvenQ[i] || i>n, 0, Function[p, p + {0, p[[1]] h[i]}][b[n - i, i]]]]];
%t A319142 a[n_] := b[n, n][[2]];
%t A319142 Array[a, 60] (* _Jean-François Alcover_, Dec 12 2020, after _Alois P. Heinz_ *)
%Y A319142 Cf. A000009, A070939.
%K A319142 nonn
%O A319142 1,2
%A A319142 _David S. Newman_, Sep 11 2018