A319142 - OEIS

%I #15 Dec 12 2020 14:17:38

%S 1,2,5,7,12,19,26,36,52,71,92,124,158,204,265,331,413,522,641,791,976,

%T 1184,1435,1741,2093,2506,3005,3574,4237,5030,5928,6971,8202,9593,

%U 11212,13087,15210,17653,20472,23665,27308,31488,36205,41570,47701,54584,62387

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

%H Alois P. Heinz, <a href="/A319142/b319142.txt">Table of n, a(n) for n = 1..10000</a>

%p h:= proc(n) option remember; 1+ilog2(n) end:

%p b:= proc(n, i) option remember; `if`(n=0, [1, 0],

%p       `if`(i<1, 0, b(n, i-1-irem(i, 2))+`if`(i::even

%p        or i>n, 0, (p-> p+[0, p[1]*h(i)])(b(n-i, i)))))

%p     end:

%p a:= n-> b(n$2)[2]:

%p seq(a(n), n=1..60);  # _Alois P. Heinz_, Sep 27 2018

%t h[n_] := h[n] = 1 + Floor@Log[2, n];

%t 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 a[n_] := b[n, n][[2]];

%t Array[a, 60] (* _Jean-François Alcover_, Dec 12 2020, after _Alois P. Heinz_ *)

%Y Cf. A000009, A070939.

%K nonn

%O 1,2

%A _David S. Newman_, Sep 11 2018