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A130848
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Periodic sequence with period (2, 5, 3, -2, -5, -3).
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1
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2, 5, 3, -2, -5, -3, 2, 5, 3, -2, -5, -3, 2, 5, 3, -2, -5, -3, 2, 5, 3, -2, -5, -3, 2, 5, 3, -2, -5, -3, 2, 5, 3, -2, -5, -3, 2, 5, 3, -2, -5, -3, 2, 5, 3, -2, -5, -3, 2, 5, 3, -2, -5, -3, 2, 5, 3, -2, -5, -3, 2, 5, 3, -2, -5, -3, 2, 5, 3, -2, -5, -3, 2, 5, 3, -2, -5, -3, 2, 5, 3, -2, -5, -3, 2, 5, 3, -2, -5, -3, 2, 5, 3, -2, -5, -3, 2, 5, 3, -2, -5, -3
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Also binomial transform of periodic sequence with period (2, 3, -5).
Sequence is identical to its third differences.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (1,-1).
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FORMULA
| For n > 1, a(n) = a(n-1)-a(n-2).
a(0) = 2; a(1) = 5; a(2) = 3; a(3) = -2; a(4) = -5; a(5) = -3; for n > 5, a(n) = a(n-6).
G.f.: (2+3*x)/(1-x+x^2).
a(n)=(1/6)*{-5*(n mod 6)-2*[(n+1) mod 6]+3*[(n+2) mod 6]+5*[(n+3) mod 6]+2*[(n+4) mod 6]-3*[(n+5) mod 6]}, with n>=0 - Paolo P. Lava (paoloplava(AT)gmail.com), Aug 01 2007
a(n) = 2*cos(1/3*Pi*n)+8/3*3^(1/2)*sin(1/3*Pi*n). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 15 2007
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PROG
| (PARI) {m=104; a=2; b=5; print1(a=2, ", ", b=5, ", "); for(n=2, m, print1(c=b-a, ", "); a=b; b=c)} /* Klaus Brockhaus, Jul 30 2007 */
(MAGMA) m:=105; [ [2, 5, 3, -2, -5, -3][ (n-1) mod 6 + 1 ]: n in [1..m] ]; /* Klaus Brockhaus, Jul 30 2007 */
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CROSSREFS
| Sequence in context: A188923 A078375 A065261 * A156637 A195784 A163766
Adjacent sequences: A130845 A130846 A130847 * A130849 A130850 A130851
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KEYWORD
| sign,easy
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AUTHOR
| Paul Curtz (bpcrtz(AT)free.fr), Jul 21 2007
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EXTENSIONS
| Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 30 2007
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