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A062882
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a(n+1)=(1-2*cos(1/9*Pi))^n+(1+2*cos(2/9*Pi))^n+(1+2*cos(4/9*Pi))^n.
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2
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4, 3, 9, 18, 45, 108, 270, 675, 1701, 4293, 10854, 27459, 69498, 175932, 445419, 1127763, 2855493, 7230222, 18307377, 46355652, 117376290, 297206739, 752553261, 1905530913, 4824972522, 12217257783, 30935180610, 78330624264
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| (Start) Let U be the unit-primitive matrix (see [Jeffery])
U=U_(9,2)=
(0 0 1 0)
(0 1 0 1)
(1 0 1 1)
(0 1 1 1).
Then a(n)=Trace(U^n). L. Edson Jeffery, April 5, 2011 (End)
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,200
L. E. Jeffery, Unit-primitive matrices
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FORMULA
| G.f.: (4-9*x+3*x^3)/(1-3*x+3*x^3). The terms in parentheses in the definition are the roots of x^3-3*x^2+3. - Ralf Stephan, Apr 10 2004
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MAPLE
| Digits := 1000:q := seq(floor(evalf((1-2*cos(1/9*Pi))^n+(1+2*cos(2/9*Pi))^n+(1+2*cos(4/9*Pi))^n)), n=1..50);
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PROG
| (PARI) { default(realprecision, 200); for (n=1, 200, a=(1 - 2*cos(1/9*Pi))^n + (1 + 2*cos(2/9*Pi))^n + (1 + 2*cos(4/9*Pi))^n; write("b062882.txt", n, " ", round(a)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 12 2009]
(PARI) Vec((4-9*x+3*x^3)/(1-3*x+3*x^3)+O(x^66)) /* Joerg Arndt, Apr 08 2011 */
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CROSSREFS
| Cf. A033304, A062883.
Sequence in context: A197694 A103218 A107381 * A132192 A147756 A075563
Adjacent sequences: A062879 A062880 A062881 * A062883 A062884 A062885
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KEYWORD
| easy,nonn,changed
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 27 2001
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EXTENSIONS
| More terms from Sascha Kurz (sascha.kurz(AT)uni-bayreuth.de), Mar 24 2002
Corrected formula, denominator of g.f. and modified g.f. (and offset) to accomodate added initial term a(0)=4. - L. Edson Jeffery, April 5, 2011.
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