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Search: id:A106249
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| A106249 |
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Expansion of (1-x+x^2+x^3)/(1-x-x^4+x^5). |
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+0
4
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| 1, 0, 1, 2, 3, 2, 3, 4, 5, 4, 5, 6, 7, 6, 7, 8, 9, 8, 9, 10, 11, 10, 11, 12, 13, 12, 13, 14, 15, 14, 15, 16, 17, 16, 17, 18, 19, 18, 19, 20, 21, 20, 21, 22, 23, 22, 23, 24, 25, 24, 25, 26, 27, 26, 27, 28, 29, 28, 29, 30, 31, 30, 31, 32, 33, 32, 33, 34, 35, 34, 35, 36, 37, 36, 37, 38
(list; graph; listen)
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OFFSET
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0,4
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FORMULA
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G.f.: (1-x+x^2+x^3)/(1-x-x^4+x^5)=(1+x^2+2x^3+x^4+2x^5+x^6)/(1-x^4)^2; a(n)=sum{k=0..n, -mu(k mod 4)}; a(n)=cos(pi*n/2)/2-sin(pi*n/2)/2+(-1)^n/4+(2n+1)/4.
a(n)=sum{k=0..n, Jacobi(2^k, 2k+1)} [Conjecture]; - Paul Barry (pbarry(AT)wit.ie), Jul 23 2005
a(n)=sum{k=0..n, Product{j=1..k, ((-1)^j)^(k-j+1)}}; - Paul Barry (pbarry(AT)wit.ie), Nov 09 2007
a(n)=A083219(n-1), n>0. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 28 2008]
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CROSSREFS
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Cf. A008611.
Sequence in context: A095207 A065362 A083219 this_sequence A110516 A134986 A162751
Adjacent sequences: A106246 A106247 A106248 this_sequence A106250 A106251 A106252
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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), Apr 27 2005
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