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A350093
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a(n) = Sum_{k=0..n} n OR k where OR is the bitwise logical OR operator (A003986).
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4
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0, 2, 7, 12, 26, 34, 45, 56, 100, 114, 131, 148, 174, 194, 217, 240, 392, 418, 447, 476, 514, 546, 581, 616, 684, 722, 763, 804, 854, 898, 945, 992, 1552, 1602, 1655, 1708, 1770, 1826, 1885, 1944, 2036, 2098, 2163, 2228, 2302, 2370, 2441, 2512, 2712, 2786, 2863
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OFFSET
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0,2
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COMMENTS
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The effect of n OR k is to force a 1-bit at all bit positions where n has a 1-bit, which means n*(n+1) in the sum. Bits of k where n has a 0-bit are NOT(n) AND k = n CNIMPL k so that a(n) = A350094(n) + n*(n+1).
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LINKS
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FORMULA
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a(n) = ((3*n+2)*n + A001196(n)) / 4.
a(2*n) = 4*a(n) - n.
a(2*n+1) = 4*a(n) + 2*n + 2.
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PROG
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(PARI) a(n) = (3*(n^2 + fromdigits(binary(n), 4)) + 2*n) >> 2;
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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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