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A130483
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a(n) = Sum_{k=0..n} (k mod 5) (Partial sums of A010874).
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26
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0, 1, 3, 6, 10, 10, 11, 13, 16, 20, 20, 21, 23, 26, 30, 30, 31, 33, 36, 40, 40, 41, 43, 46, 50, 50, 51, 53, 56, 60, 60, 61, 63, 66, 70, 70, 71, 73, 76, 80, 80, 81, 83, 86, 90, 90, 91, 93, 96, 100, 100, 101, 103, 106, 110, 110, 111, 113, 116, 120, 120, 121, 123, 126, 130, 130
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OFFSET
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0,3
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COMMENTS
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Let A be the Hessenberg n X n matrix defined by: A[1,j]=j mod 5, A[i,i]=1, A[i,i-1]=-1. Then, for n>=1, a(n)=det(A). - Milan Janjic, Jan 24 2010
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LINKS
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FORMULA
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G.f.: x*(1 + 2*x + 3*x^2 + 4*x^3)/((1-x^5)*(1-x)).
a(n) = a(n-5) - a(n-6) for n>5; a(n) = a(n-5) + 10 for n>4.
a(n) = 10 + Sum_{k=1..4} k*floor((n-k)/5). (End)
a(n) = ((n mod 5)^2 - 3*(n mod 5) + 4*n)/2. - Ammar Khatab, Aug 13 2020
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MAPLE
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seq(coeff(series(x*(1+2*x+3*x^2+4*x^3)/((1-x^5)*(1-x)), x, n+1), x, n), n = 0..70); # G. C. Greubel, Aug 31 2019
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MATHEMATICA
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Accumulate[Mod[Range[0, 70], 5]] (* or *) Accumulate[PadRight[{}, 70, {0, 1, 2, 3, 4}]] (* Harvey P. Dale, Nov 11 2016 *)
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PROG
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(Magma) I:=[0, 1, 3, 6, 10, 10]; [n le 6 select I[n] else Self(n-1) + Self(n-5) - Self(n-6): n in [1..71]]; // G. C. Greubel, Aug 31 2019
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P(x*(1+2*x+3*x^2+4*x^3)/((1-x^5)*(1-x))).list()
(GAP) a:=[0, 1, 3, 6, 10, 10];; for n in [7..71] do a[n]:=a[n-1]+a[n-5]-a[n-6]; od; a; # G. C. Greubel, Aug 31 2019
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CROSSREFS
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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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