OFFSET
1,4
COMMENTS
The defining [sum] is equivalent to
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a(n)=[n(n+1)r/2]-sum{[k*r] : 1<=k<=n},
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where []=floor and r=sqrt(2). Let s(n) denote the n-th partial sum of the sequence a; then the difference sequence d defined by d(n)=s(n+1)-s(n) gives the runlengths of a.
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Examples:
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r...........a........s....
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..5000
EXAMPLE
a(5)=[(e)+(2e)+(3e)+4(e)+5(e)]
=[.718+.436+.154+.873+.591]
=[2.77423]=2.
MATHEMATICA
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Aug 19 2011
STATUS
approved