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A048644
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Differences between partial sums of Gray code (A048641) and triangular numbers (A000217).
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2
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0, 0, 1, 0, 2, 4, 3, 0, 4, 8, 13, 16, 14, 12, 7, 0, 8, 16, 25, 32, 42, 52, 59, 64, 60, 56, 53, 48, 38, 28, 15, 0, 16, 32, 49, 64, 82, 100, 115, 128, 148, 168, 189, 208, 222, 236, 247, 256, 248, 240, 233, 224, 218, 212, 203, 192, 172, 152, 133, 112, 86, 60, 31, 0, 32, 64
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OFFSET
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0,5
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COMMENTS
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a(2^n-1) = 0 for all n.
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LINKS
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FORMULA
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a(n) = sum(XORnos(j, floor(j/2)), j=0..n)-((n^2+n)/2).
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MATHEMATICA
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{0}~Join~MapIndexed[#1 - PolygonalNumber[First[#2]] &, Accumulate[Array[BitXor[#, Floor[#/2]] &, 65]]] (* Michael De Vlieger, Oct 29 2022 *)
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PROG
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(PARI) a(n) = sum(k=0, n, bitxor(k, k>>1)) - n*(n+1)/2; \\ Michel Marcus, Oct 02 2015
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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