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Search: id:A130707
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| A130707 |
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a(n+3)=3*[a(n+2)-a(n+1)]+2*a(n). |
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+0
3
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| 1, 2, 2, 2, 4, 10, 22, 44, 86, 170, 340, 682, 1366, 2732, 5462, 10922, 21844, 43690, 87382, 174764, 349526, 699050, 1398100, 2796202, 5592406, 11184812, 22369622, 44739242, 89478484, 178956970, 357913942, 715827884, 1431655766, 2863311530
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Binomial transform of period-3 sequence with period 1 1 -1.
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FORMULA
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a(n)=2^n/3 + 4(-1)^n*(1/3)*cos((2n+1)Pi/3). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 27 2007
G.f.: (-1+x+x^2)/(2*x-1)/(x^2-x+1). a(n) = [2*A057079(n)+2^n]/3. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 18 2007
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MAPLE
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a:=proc(n) options operator, arrow: (1/3)*2^n+(4/3)*(-1)^n*cos((1/3)*(2*n+1)*Pi) end proc: seq(a(n), n = 0 .. 33); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 27 2007
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CROSSREFS
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Sequence in context: A160179 A021822 A153986 this_sequence A131562 A107902 A142974
Adjacent sequences: A130704 A130705 A130706 this_sequence A130708 A130709 A130710
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KEYWORD
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nonn
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AUTHOR
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Paul Curtz (bpcrtz(AT)free.fr), Jul 01 2007
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 27 2007
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