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A130486
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Sum {0<=k<=n, k mod 8} (Partial sums of A010877).
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12
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0, 1, 3, 6, 10, 15, 21, 28, 28, 29, 31, 34, 38, 43, 49, 56, 56, 57, 59, 62, 66, 71, 77, 84, 84, 85, 87, 90, 94, 99, 105, 112, 112, 113, 115, 118, 122, 127, 133, 140, 140, 141, 143, 146, 150, 155, 161, 168, 168, 169, 171, 174, 178, 183, 189, 196, 196, 197, 199, 202, 206
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Let A be the Hessenberg n by n matrix defined by: A[1,j]=j mod 8, A[i,i]:=1, A[i,i-1]=-1.Then, for n>=1, a(n)=det(A). [From Milan R. Janjic (agnus(AT)blic.net), Jan 24 2010]
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FORMULA
| a(n)=28*floor(n/8)+A010877(n)*(A010877(n)+1)/2. G.f.: g(x)=(sum{1<=k<8, k*x^k})/((1-x^8)(1-x)). Also: g(x)=x(7x^8-8x^7+1)/((1-x^8)(1-x)^3).
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MAPLE
| a:=n->add(chrem( [n, j], [1, 8] ), j=1..n):seq(a(n), n=0..60); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 07 2009]
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CROSSREFS
| Cf. A010872, A010873, A010874, A010875, A010876, A010878. A130481, A130482, A130483, A130484, A130485, A130487.
Sequence in context: A171971 A184009 A105334 * A054636 A124158 A161208
Adjacent sequences: A130483 A130484 A130485 * A130487 A130488 A130489
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KEYWORD
| nonn
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AUTHOR
| Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 31 2007
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