A309371 a(n) = Sum_{k=1..n} k * A088370(n,k).

0, 1, 5, 13, 29, 48, 82, 122, 186, 239, 327, 419, 559, 674, 852, 1028, 1284, 1453, 1721, 1977, 2353, 2636, 3062, 3462, 4030, 4403, 4971, 5495, 6243, 6790, 7592, 8328, 9352, 9945, 10861, 11685, 12869, 13704, 14938, 16050, 17602, 18567, 20015, 21307, 23127, 24410

Offset: 0

Author

Alois P. Heinz, Jul 25 2019

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000292, A000330, A088370.

Programs

Maple

b:= proc(n) option remember; `if`(n<2, n, (h->
      [map(x-> 2*x-1, [b(n-h)])[],
       map(x-> 2*x, [b(h)])[]][])(iquo(n, 2)))
    end:
a:= n-> (l-> add(i*l[i], i=1..n))([b(n)]):
seq(a(n), n=0..50);

Mathematica

T[n_] := T[n] = If[n == 1, {1}, Join[q = Quotient[n, 2];
   2*T[n - q] - 1, 2*T[q]]];
a[n_] := Sum[k*T[n][[k]], {k, 1, n}];
Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Sep 15 2022, after Alois P. Heinz in A088370 *)

Formula

a(n) = Sum_{k=1..n} k * A088370(n,k).

A000292(n) <= a(n) <= A000330(n).