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- #!/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
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