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A129080
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Palindromic complexity sequence based on A095263.
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1
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4, 8, 14, 25, 48, 99, 215, 482, 1100, 2534, 5865, 13606, 31599, 73425, 170656, 396688, 922146, 2143685, 4983416, 11584987, 26931775, 62608726, 145547572, 338356994, 786584517
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Definition of palindromic complexity sequence from Frougny et al.: P(n+1)+P(n)=C(n+1)-C(n)+2. From that is derived: P(n)=P(n-1)+C(n)-C(n-1)+2. I used the Adamson-Akiyama sofic with characteristic polynomial: ( a count down Pisot) x^3-3*x^2+2*x-1
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REFERENCES
| Shigeki Akiyama, Pisot number syetem and its dual tiling, `Physics and Theoretical Computer Science', ed. by J.P. Gazeau et al., IOS Press (2007) 133-154. : http://mathweb.sc.niigata-u.ac.jp/~akiyama/Research2.html
Petr Ambroz, Christiane Frougny, Zuzana Masakova and Edita Pelantova, Palindromic complexity of infinite words associated with simple Parry numbers, arXiv:math/0603608.
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FORMULA
| a(n) = a[n - 1] + A095263[n] - A095263[n - 1] + 2
G.f.: -x*(x^4-5*x^3+10*x^2-12*x+4)/((x^3-2*x^2+3*x-1)*(x-1)^2) [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 14 2009]
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MATHEMATICA
| (* A095263*) a[1] = 1; a[2] = 3; a[3] = 7; a[n_] := a[n] = 3a[n - 1] - 2a[n - 2] + a[n - 3]; Table[a[n], {n, 22}] (* Palindrome*) P[1] = 4; P[n_] := P[n] = P[n - 1] + a[n] - a[n - 1] + 2; Table[P[n], {n, 1, 25}]
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CROSSREFS
| Cf. A095263.
Sequence in context: A105143 A020185 A008029 * A138643 A183977 A153364
Adjacent sequences: A129077 A129078 A129079 * A129081 A129082 A129083
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KEYWORD
| nonn,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), May 11 2007
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EXTENSIONS
| G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009.
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