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Search: id:A117447
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| A117447 |
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Expansion of (1+2x+3x^2+x^3)/(1+x-x^3-x^4). |
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+0
2
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| 1, 1, 2, 0, 2, 1, 1, 1, 2, 0, 2, 1, 1, 1, 2, 0, 2, 1, 1, 1, 2, 0, 2, 1, 1, 1, 2, 0, 2, 1, 1, 1, 2, 0, 2, 1, 1, 1, 2, 0, 2, 1, 1, 1, 2, 0, 2, 1, 1, 1, 2
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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The sequence a(n+3) is periodic {0,2,1,1,1,2} with g.f. x(2+3x+2x^2)/(1+x-x^3-x^4). Row sums of number triangle A117446.
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FORMULA
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G.f.: 1+x+2x^2+x^4(2+3x+2x^2)/(1+x-x^3-x^4); a(n)=sum{k=0..n, C(L(k/3),n-k)}, where L(j/p) is the Legendre symbol of j and p.
a(n)=1/90*{7*(n mod 6)+22*[(n+1) mod 6]-23*[(n+2) mod 6]+37*[(n+3) mod 6]-8*[(n+4) mod 6]+7*[(n+5) mod 6]} with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Nov 21 2006
a(n)=7/6 - 1/2*( - 1)^n - 2/3*cos(2*Pi*n/3) [From Richard Choulet (richardchoulet(AT)yahoo.fr), Dec 12 2008]
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CROSSREFS
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Sequence in context: A135220 A068320 A111330 this_sequence A053250 A160813 A116664
Adjacent sequences: A117444 A117445 A117446 this_sequence A117448 A117449 A117450
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Mar 16 2006
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