A230088 Partial sums of A010062.

1, 3, 6, 11, 18, 28, 40, 54, 71, 90, 112, 137, 165, 196, 232, 270, 311, 355, 402, 454, 509, 569, 633, 698, 765, 835, 908, 984, 1063, 1147, 1234, 1326, 1422, 1520, 1621, 1726, 1835, 1949, 2067, 2190, 2319, 2450, 2584, 2721, 2861, 3004, 3152, 3303, 3459, 3619

Offset: 0

Author

N. J. A. Sloane, Oct 08 2013

Keywords

• nonn
• base

Links

• Robert Israel, Table of n, a(n) for n = 0..10000
• Kenneth B. Stolarsky, The sum of a digitaddition series, Proc. Amer. Math. Soc. 59 (1976), no. 1, 1--5. MR0409340 (53 #13099).

Crossrefs

Cf. A010062.

Programs

Maple

f:= proc(n) option remember;
  procname(n-1)+convert(convert(procname(n-1),base,2),`+`)
end proc:
f(0):= 1:
g:= proc(n) option remember;
procname(n-1)+f(n)
end proc:
g(0):= 1:
map(g, [$0..100]); # Robert Israel, Jul 07 2020

PARI

lista(nn) = {a = 1;sa = 0; for (n=2, nn, sa += a; print1(sa, ", "); a += hammingweight(a););} \\ Michel Marcus, Apr 04 2015

Formula

a(n) ~ (n^2/4)*log_2(n). [Stolarsky]

Extensions

More terms from Michel Marcus, Apr 04 2015