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A130481
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Sum {0<=k<=n, k mod 3} (Partial sums of A010872).
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27
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0, 1, 3, 3, 4, 6, 6, 7, 9, 9, 10, 12, 12, 13, 15, 15, 16, 18, 18, 19, 21, 21, 22, 24, 24, 25, 27, 27, 28, 30, 30, 31, 33, 33, 34, 36, 36, 37, 39, 39, 40, 42, 42, 43, 45, 45, 46, 48, 48, 49, 51, 51, 52, 54, 54, 55, 57, 57, 58, 60, 60, 61, 63, 63, 64, 66, 66, 67, 69, 69, 70, 72, 72
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Essentially the same as A092200. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 13 2008
Let A be the Hessenberg n by n matrix defined by: A[1,j]=j mod 3, 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 (1,0,1,-1).
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FORMULA
| a(n)=3*floor(n/3)+A010872(n)*(A010872(n)+1)/2. G.f.: g(x)=(2x^2+x)/((1-x^3)(1-x)).
a(n)= n+1-(Fibonacci(n+1) mod 2). [From Gary Detlefs (gdetlefs(AT)aol.com) Mar 13 2011]
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MAPLE
| a:=n->add(chrem( [n, j], [1, 3] ), j=1..n):seq(a(n), n=0..72); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 07 2009]
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CROSSREFS
| Cf. A010872, A010873, A010874, A010875, A010876, A010877, A130482, A130483, A130484.
Sequence in context: A074883 A196245 A092200 * A145805 A098238 A088651
Adjacent sequences: A130478 A130479 A130480 * A130482 A130483 A130484
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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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