A335063 a(n) = Sum_{k=0..n} (binomial(n,k) mod 2) * k.
0, 1, 2, 6, 4, 10, 12, 28, 8, 18, 20, 44, 24, 52, 56, 120, 16, 34, 36, 76, 40, 84, 88, 184, 48, 100, 104, 216, 112, 232, 240, 496, 32, 66, 68, 140, 72, 148, 152, 312, 80, 164, 168, 344, 176, 360, 368, 752, 96, 196, 200, 408, 208, 424, 432, 880, 224, 456, 464, 944, 480
Offset: 0
Keywords
Links
- Robert Israel, Table of n, a(n) for n = 0..3000
Programs
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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
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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] -
PARI
a(n) = n*2^(hammingweight(n)-1); \\ Michel Marcus, May 22 2020
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