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A130484
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Sum {0<=k<=n, k mod 6} (Partial sums of A010875).
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21
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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 by 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). [From Milan Janjic, Jan 24 2010]
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LINKS
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Table of n, a(n) for n=0..62.
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FORMULA
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a(n)=15*floor(n/6)+A010875(n)*(A010875(n)+1)/2. G.f.: g(x)=(sum{1<=k<6, k*x^k})/((1-x^6)(1-x)). Also: g(x)=x(5x^6-6x^5+1)/((1-x^6)(1-x)^3).
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MAPLE
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a:=n->add(chrem( [n, j], [1, 6] ), j=1..n):seq(a(n), n=0..62); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 07 2009]
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MATHEMATICA
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f[n_]:=Mod[n, 6]; s=0; lst={}; Do[AppendTo[lst, s+=f[n]], {n, 0, 5!}]; lst [From Vladimir Joseph Stephan Orlovsky, Feb 07 2010]
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CROSSREFS
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Cf. A010872, A010873, A010874, A010876, A010877. A130481, A130482, A130483, A130485.
Sequence in context: A194101 A105333 A126234 * A074374 A109804 A120993
Adjacent sequences: A130481 A130482 A130483 * A130485 A130486 A130487
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KEYWORD
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nonn
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AUTHOR
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Hieronymus Fischer, May 31 2007
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STATUS
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approved
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