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A163577
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Count of indices x in [0,n] that satisfy the equation A000120(x) + A000120(n-x) = A000120(n) + 2.
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4
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0, 0, 0, 0, 2, 0, 1, 0, 2, 4, 1, 0, 5, 2, 2, 0, 2, 4, 5, 8, 5, 2, 4, 0, 5, 10, 4, 4, 10, 4, 4, 0, 2, 4, 5, 8, 9, 10, 12, 16, 5, 10, 6, 4, 12, 8, 8, 0, 5, 10, 12, 20, 12, 8, 12, 8, 10, 20, 8, 8, 20, 8, 8, 0, 2, 4, 5, 8, 9, 10, 12, 16, 9, 18, 14, 20, 20, 24, 24, 32, 5, 10, 14, 20, 14, 12, 16, 8, 12, 24
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OFFSET
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0,5
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COMMENTS
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For every solution x, binomial(n,x) is 4 times an odd integer.
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LINKS
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EXAMPLE
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For n=8, there are a(8)=2 solutions, namely x=2 and x=6.
For n=9, there are a(9)=4 solutions, namely x=2, 3, 6 and 7.
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MAPLE
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read("transforms") ; A000120 := proc(n) wt(n) ; end:
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MATHEMATICA
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a120[n_] := DigitCount[n, 2, 1]; a[n_] := Count[Range[0, n], x_ /; a120[x] + a120[n-x] == a120[n]+2]; Array[a, 90, 0] (* Jean-François Alcover, Jul 10 2017 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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Extended beyond a(22), examples added by R. J. Mathar, Jul 08 2009
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STATUS
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approved
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