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A130488
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Sum {0<=k<=n, k mod 10} (Partial sums of A010879).
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7
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0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 45, 46, 48, 51, 55, 60, 66, 73, 81, 90, 90, 91, 93, 96, 100, 105, 111, 118, 126, 135, 135, 136, 138, 141, 145, 150, 156, 163, 171, 180, 180, 181, 183, 186, 190, 195, 201, 208, 216, 225, 225, 226, 228, 231, 235, 240, 246, 253
(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 10, 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)=45*floor(n/10)+A010879(n)*(A010879(n)+1)/2. G.f.: g(x)=(sum{1<=k<10, k*x^k})/((1-x^10)(1-x)). Also: g(x)=x(9x^10-10x^9+1)/((1-x^10)(1-x)^3).
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MAPLE
| a:=n->add(chrem( [n, j], [1, 10] ), j=1..n):seq(a(n), n=0..57); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 07 2009]
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CROSSREFS
| Cf. A010872, A010873, A010874, A010875, A010876, A010877, A010878. A130481, A130482, A130483, A130484, A130485, A130486, A130487.
Sequence in context: A033441 A107082 A187845 * A061076 A054632 A109453
Adjacent sequences: A130485 A130486 A130487 * A130489 A130490 A130491
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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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