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A350094
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a(n) = Sum_{k=0..n} n CNIMPL k where CNIMPL = NOT(n) AND k is the bitwise logical converse non-implication operator (A102037).
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3
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0, 0, 1, 0, 6, 4, 3, 0, 28, 24, 21, 16, 18, 12, 7, 0, 120, 112, 105, 96, 94, 84, 75, 64, 84, 72, 61, 48, 42, 28, 15, 0, 496, 480, 465, 448, 438, 420, 403, 384, 396, 376, 357, 336, 322, 300, 279, 256, 360, 336, 313, 288, 270, 244, 219, 192, 196, 168, 141, 112
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OFFSET
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0,5
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COMMENTS
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The effect of NOT(n) AND k is to retain from k only those bits where n has a 0-bit. Conversely n AND k retains from k those bits where n has a 1-bit. Together they are all bits of k so that a(n) + A222423(n) = Sum_{k=0..n} k = n*(n+1)/2.
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LINKS
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FORMULA
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a(2*n) = 4*a(n) + n.
a(2*n+1) = 4*a(n).
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MAPLE
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with(Bits): cnimp := (n, k) -> And(Not(n), k):
seq(add(cnimp(n, k), k = 0..n), n = 0..59); # Peter Luschny, Dec 14 2021
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PROG
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(PARI) a(n) = (3*fromdigits(binary(n), 4) - n^2 - 2*n)/4;
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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STATUS
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approved
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