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A131242
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Partial sums of A059995: a(n) = sum_{k=0..n} floor(k/10).
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18
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 156, 162, 168, 174, 180, 186, 192, 198
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OFFSET
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0,12
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COMMENTS
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,0,0,0,1,-2,1).
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FORMULA
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a(n) = (1/2)*floor(n/10)*(2n-8-10*floor(n/10)).
G.f.: x^10/((1-x^10)(1-x)^2).
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EXAMPLE
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As square array :
0, 0, 0, 0, 0, 0, 0, 0, 0, 0
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
12, 14, 16, 18, 20, 22, 24, 26, 28, 30
33, 36, 39, 42, 45, 48, 51, 54, 57, 60
64, 68, 72, 76, 80, 84, 88, 92, 96, 100
105, 110, 115, 120, 125, 130, 135, 140, 145, 150
156, 162, 168, 174, 180, 186, 192, 198, 204, 210
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MATHEMATICA
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Table[(1/2)*Floor[n/10]*(2*n - 8 - 10*Floor[n/10]), {n, 0, 50}] (* G. C. Greubel, Dec 13 2016 *)
Accumulate[Table[FromDigits[Most[IntegerDigits[n]]], {n, 0, 110}]] (* or *) LinearRecurrence[{2, -1, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2}, 120] (* Harvey P. Dale, Apr 06 2017 *)
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PROG
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(PARI) for(n=0, 50, print1((1/2)*floor(n/10)*(2n-8-10*floor(n/10)), ", ")) \\ G. C. Greubel, Dec 13 2016
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CROSSREFS
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Cf. A008728, A059995, A010879, A002266, A130488, A000217, A002620, A130518, A130519, A130520, A174709, A174738, A118729, A218470.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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