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A053539
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a(n) = n * 8^(n-1).
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5
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0, 1, 16, 192, 2048, 20480, 196608, 1835008, 16777216, 150994944, 1342177280, 11811160064, 103079215104, 893353197568, 7696581394432, 65970697666560, 562949953421312, 4785074604081152, 40532396646334464, 342273571680157696
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OFFSET
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0,3
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COMMENTS
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The Szeged index of the hypercube Q_n (see the Ashrafi et al. reference (p. 45, last line). - Emeric Deutsch, Aug 06 2014
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REFERENCES
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Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
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LINKS
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FORMULA
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a(n) = 16*a(n-1) - 64*a(n-2), with a(0)=0, a(1)=1. - Emeric Deutsch, Aug 06 2014
G.f.: x/(1-8*x)^2.
E.g.f.: x*exp(8*x). (End)
Sum_{n>=1} 1/a(n) = 8*log(8/7).
Sum_{n>=1} (-1)^(n+1)/a(n) = 8*log(9/8). (End)
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MAPLE
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a := proc(n) option remember; if n<2 then n else 16*a(n-1)-64*a(n-2) end if end proc: seq(a(n), n = 0 .. 20); # Emeric Deutsch, Aug 06 2014
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MATHEMATICA
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Table[n 8^(n-1), {n, 0, 20}] (* or *) LinearRecurrence[{16, -64}, {0, 1}, 20] (* Harvey P. Dale, Feb 01 2017 *)
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PROG
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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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