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A130482
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Sum {0<=k<=n, k mod 4} (Partial sums of A010873).
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25
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0, 1, 3, 6, 6, 7, 9, 12, 12, 13, 15, 18, 18, 19, 21, 24, 24, 25, 27, 30, 30, 31, 33, 36, 36, 37, 39, 42, 42, 43, 45, 48, 48, 49, 51, 54, 54, 55, 57, 60, 60, 61, 63, 66, 66, 67, 69, 72, 72, 73, 75, 78, 78, 79, 81, 84, 84, 85, 87, 90, 90, 91, 93, 96, 96, 97, 99, 102, 102, 103, 105
(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 4, 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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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (1,0,0,1,-1).
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FORMULA
| a(n)=6*floor(n/4)+A010873(n)*(A010873(n)+1)/2. G.f.: g(x)=(3x^3+2x^2+x)/((1-x^4)(1-x)).
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MAPLE
| a:=n->add(chrem( [n, j], [1, 4] ), j=1..n):seq(a(n), n=0..70); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 07 2009]
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MATHEMATICA
| f[n_]:=Mod[n, 4]; s=0; lst={}; Do[AppendTo[lst, s+=f[n]], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 07 2010]
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CROSSREFS
| Cf. A010872, A010874, A010875, A010876, A010877. A130481, A130483, A130484, A130485.
Sequence in context: A079093 A153035 A072910 * A177783 A178746 A025500
Adjacent sequences: A130479 A130480 A130481 * A130483 A130484 A130485
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KEYWORD
| nonn,easy
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AUTHOR
| Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 29 2007
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