prog.sf

#!/usr/bin/ruby

# Number of 0's minus number of 1's among the edge truncated binary representations of the first n positive integers.

# Cf. A037861, A301336, A308430.

# Formula:
#   a(n) = Sum_{k=2..n} (A037861(n) + (1 - (-1)^n))

# (PARI) a(n) = sum(k=2, n, #binary(k) - 2*hammingweight(k) + (1 - (-1)^k))

# See also:
#   https://oeis.org/A037861
#   https://oeis.org/A301336
#   https://oeis.org/A308430

func A037861(n) {
   var t = n.as_bin
   (t.count('0') - t.count('1'))
}

func f(n) {
   # var t = n.as_bin
   # (t.count('0') - t.count('1')) #+ (n.is_odd ? 2 : 0)

   if (n <= 1) {
       return 0
   }

   # n.is_odd ? 2+A037861(n) : A037861(n)

   #A037861(n) + (1 - (-1)**n)
   A037861(n) + (1 - (-1)**n)
}

101.of(f).accumulate.each{.say}

# Program for A301336:
#   a(n) = sum(k=2, n, 2*hammingweight(k) - #binary(k)); \\ for n >0