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A130484
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a(n) = Sum_{k=0..n} (k mod 6) (Partial sums of A010875).
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22
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0, 1, 3, 6, 10, 15, 15, 16, 18, 21, 25, 30, 30, 31, 33, 36, 40, 45, 45, 46, 48, 51, 55, 60, 60, 61, 63, 66, 70, 75, 75, 76, 78, 81, 85, 90, 90, 91, 93, 96, 100, 105, 105, 106, 108, 111, 115, 120, 120, 121, 123, 126, 130, 135, 135, 136, 138, 141, 145, 150, 150, 151, 153
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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 6, 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.: (Sum_{k=1..5} k*x^k)/((1-x^6)*(1-x)) = x*(1 - 6*x^5 + 5*x^6)/((1-x^6)*(1-x)^3).
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MAPLE
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seq(coeff(series(x*(1-6*x^5+5*x^6)/((1-x^6)*(1-x)^3), 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], 6]] (* or *) Accumulate[PadRight[ {}, 70, Range[0, 5]]] (* Harvey P. Dale, Jul 12 2016 *)
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PROG
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(Magma) I:=[0, 1, 3, 6, 10, 15, 15]; [n le 7 select I[n] else Self(n-1) + Self(n-6) - Self(n-7): n in [1..71]]; // G. C. Greubel, Aug 31 2019
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P(x*(1-6*x^5+5*x^6)/((1-x^6)*(1-x)^3)).list()
(GAP) a:=[0, 1, 3, 6, 10, 15, 15];; for n in [8..71] do a[n]:=a[n-1]+a[n-6]-a[n-7]; 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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