OFFSET
0,3
COMMENTS
Modulo 2 binomial transform of nonnegative integers.
LINKS
Robert Israel, Table of n, a(n) for n = 0..3000
FORMULA
MAPLE
g:= proc(n, k) local L, M, t, j;
L:= convert(k, base, 2);
M:= convert(n, base, 2);
1-max(zip(`*`, L, M))
end proc:
f:= n -> add(k*g(n-k, k), k=0..n):
map(f, [$0..100]); # Robert Israel, May 24 2020
MATHEMATICA
Table[Sum[Mod[Binomial[n, k], 2] k, {k, 0, n}], {n, 0, 60}]
(* or *)
nmax = 60; CoefficientList[Series[(x/2) D[Product[(1 + 2 x^(2^k)), {k, 0, Log[2, nmax]}], x], {x, 0, nmax}], x]
PROG
(PARI) a(n) = n*2^(hammingweight(n)-1); \\ Michel Marcus, May 22 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 21 2020
STATUS
approved