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Search: id:A135448
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| A135448 |
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Period 5: repeat 1, 5, 3, 4, -2 . |
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+0
1
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| 1, 5, 3, 4, -2, 1, 5, 3, 4, -2, 1, 5, 3, 4, -2, 1, 5, 3, 4, -2, 1, 5, 3, 4, -2, 1, 5, 3, 4, -2, 1, 5, 3, 4, -2, 1, 5, 3, 4, -2, 1, 5, 3, 4, -2, 1, 5, 3, 4, -2, 1, 5, 3, 4, -2, 1, 5, 3, 4, -2, 1, 5, 3, 4, -2, 1, 5, 3, 4, -2, 1, 5, 3, 4, -2, 1, 5, 3, 4, -2, 1, 5, 3, 4, -2, 1, 5, 3, 4, -2, 1, 5, 3, 4, -2, 1
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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a(n) == 5a(n-1) mod 11.
a(n)=(1/50)*{-19*(n mod 5)+71*[(n+1) mod 5]+[(n+2) mod 5]+31*[(n+3) mod 5]-29*[(n+4) mod 5]}, with n>=0. - Paolo P. Lava (ppl(AT)spl.at), Dec 18 2007
a(n) =(11/5)-((3+2*5^0.5)/5)*cos(2*Pi*n/5)-(1/10)*((20-4*5^0.5)^0.5-7*(20+4*5^0.5)^0.5)*sin(2*Pi*n/5))-((3-2*5^0.5)/5)*cos(4*Pi*n/5)+(1/10)*((20+4*5^0.5)^0.5+7*(20-4*5^0.5)^0.5)*sin(4*Pi*n/5). G.f. h(z) = a(0)+a(1)*z+a(2)*z^2+...= ((1+5*z+3*z^2+4*z^3-2*z^4)/(1-z^5)). - Richard Choulet (richardchoulet(AT)yahoo.fr), Jan 02 2008
O.g.f.: (-1-5*x-3*x^2-4*x^3+2*x^4)/[(x-1)*(1+x+x^2+x^3+x^4)] . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 07 2008
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MAPLE
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A135448 := proc(n) op((n mod 5)+1, [1, 5, 3, 4, -2]) ; end: seq(A135448(n), n=0..150) ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 07 2009]
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CROSSREFS
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Sequence in context: A004486 A011426 A090343 this_sequence A107488 A114236 A137898
Adjacent sequences: A135445 A135446 A135447 this_sequence A135449 A135450 A135451
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KEYWORD
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sign
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AUTHOR
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Paul Curtz (bpcrtz(AT)free.fr), Dec 14 2007
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EXTENSIONS
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More periods from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 07 2009
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