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A184976
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a(n) = [e]+[2*e]+...+[n*e], where []=floor.
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1
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2, 7, 15, 25, 38, 54, 73, 94, 118, 145, 174, 206, 241, 279, 319, 362, 408, 456, 507, 561, 618, 677, 739, 804, 871, 941, 1014, 1090, 1168, 1249, 1333, 1419, 1508, 1600, 1695, 1792, 1892, 1995, 2101, 2209, 2320, 2434, 2550, 2669, 2791, 2916, 3043, 3173, 3306, 3441, 3579, 3720
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OFFSET
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1,1
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COMMENTS
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It is interesting to note that a(n)/n^2 converges to e/2 .
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LINKS
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FORMULA
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EXAMPLE
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a(3) = 15 because [2.71828...] + [2*2.71828...] + [3*2.71828...] = 2 + 5 + 8 = 15.
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MAPLE
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with(numtheory):Digits:=100:s:=0:e:=exp(1):for n from 1 to 100 do: s:=s+floor(n*e):printf(`%d,
`, s):od:
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MATHEMATICA
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Accumulate[Table[Floor[E n], {n, 60}]] (* Harvey P. Dale, Jan 14 2012 *)
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PROG
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(PARI) for(n=1, 50, print1(sum(k=1, n, floor(exp(1)*k)), ", ")) \\ G. C. Greubel, Jun 02 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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