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 A129080 Expansion of g.f. x*(x^4 - 5*x^3 + 10*x^2 - 12*x + 4)/((1-x)^2*(1 - 3*x + 2*x^2 - x^3)). 1
 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, 1828587086, 4250949167, 9882257793, 22973462076, 53406819752, 124155792838 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 Shigeki Akiyama, Pisot number system and its dual tiling, in: "Physics and Theoretical Computer Science", ed. by J. P. Gazeau et al., IOS Press (2007) 133-154. Petr Ambroz, Christiane Frougny, Zuzana Masakova and Edita Pelantova, Palindromic complexity of infinite words associated with simple Parry numbers, arXiv:math/0603608 [math.CO], 2006. Index entries for linear recurrences with constant coefficients, signature (5,-9,8,-4,1) 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)/((1-x)^2*(1 - 3*x + 2*x^2 - x^3)). [Maksym Voznyy (voznyy(AT)mail.ru), Aug 14 2009; corrected by R. J. Mathar, Sep 16 2009] a(n) = A095263(n) + 2*n + 1. - G. C. Greubel, Apr 12 2021 MAPLE m:=40; S:=series( x*(x^4-5*x^3+10*x^2-12*x+4)/((1-x)^2*(1-3*x+2*x^2-x^3)), x, m+1): seq(coeff(S, x, j), j=1..m); # G. C. Greubel, Apr 12 2021 MATHEMATICA (* b = A095263 *) b[n_]:= b[n]= If[n<4, 2^n -1, 3*b[n-1] -2*b[n-2] +b[n-3]]; a[n_]:= a[n]= If[n==1, 4, a[n-1] +b[n] -b[n-1] +2]; Table[a[n], {n, 40}] (*modified by G. C. Greubel, Apr 12 2021 *) LinearRecurrence[{5, -9, 8, -4, 1}, {4, 8, 14, 25, 48}, 40] (* Harvey P. Dale, Feb 14 2015 *) PROG (Magma) b:= func< n | n lt 4 select 2^n -1 else 3*Self(n-1) -2*Self(n-2) +Self(n-3) >; [2*n+1+b(n): n in [1..40]]; // G. C. Greubel, Apr 12 2021 (Sage) @CachedFunction def b(n): return 2^n -1 if n < 4 else 3*b(n-1) -2*b(n-2) +b(n-3) [2*n+1 +b(n) for n in (1..40)] # G. C. Greubel, Apr 12 2021 CROSSREFS Cf. A095263. Sequence in context: A105143 A020185 A008029 * A138643 A183977 A153364 Adjacent sequences: A129077 A129078 A129079 * A129081 A129082 A129083 KEYWORD nonn,easy AUTHOR Roger L. Bagula, May 11 2007 EXTENSIONS Edited by G. C. Greubel, Apr 12 2021 New name using Maksym Voznyy's g.f., Joerg Arndt, Apr 13 2021 STATUS approved

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Last modified September 21 02:47 EDT 2023. Contains 365486 sequences. (Running on oeis4.)