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A130497
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Repetition of odd numbers five times.
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0
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1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 9, 9, 9, 9, 9, 11, 11, 11, 11, 11, 13, 13, 13, 13, 13, 15, 15, 15, 15, 15, 17, 17, 17, 17, 17, 19, 19, 19, 19, 19, 21, 21, 21, 21, 21, 23, 23, 23, 23, 23, 25, 25, 25, 25, 25, 27, 27, 27, 27, 27, 29, 29, 29, 29, 29, 31, 31, 31
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,6
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FORMULA
| a(n)= -1 + 2*Sum_{k=0..n} {[8*(sin(2*Pi*k/5))^2-5]^2-5}/20, with n>=0. a(n)= -1 + 2*Sum_{k=0..n} 1/50*{-9*[k mod 5]+[(k+1) mod 5]+[(k+2) mod 5]+[(k+3) mod 5]+11*[(k+4) mod 5]}, with n>=0.
a(n)=-1+2*Sum{k=0..n}{1-(k^4 mod 5)}, with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Feb 17 2010]
a(n) = a(n-1)+a(n-5)-a(n-6). G.f.: (1+x)*(x^4-x^3+x^2-x+1)/ ((1+x+x^2+x^3+x^4) * (x-1)^2 ). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 17 2010]
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MAPLE
| P:=proc(n) local i, j, k; for i from 0 by 1 to n do j:=-1+2*sum('(8*(sin(2*Pi*k/5))^2-5)^2-5', 'k'=0..i)/20 ; print(j); od; end: P(100);
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CROSSREFS
| Cf. A129756.
Sequence in context: A204854 A113215 A105591 * A178154 A126715 A158805
Adjacent sequences: A130494 A130495 A130496 * A130498 A130499 A130500
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KEYWORD
| easy,nonn
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AUTHOR
| Paolo P. Lava & Giorgio Balzarotti (paoloplava(AT)gmail.com), May 31 2007
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EXTENSIONS
| Corrected formula by Paolo P. Lava (paoloplava(AT)gmail.com), Feb 17 2010
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