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A003476
a(n) = a(n-1) + 2*a(n-3).
(Formerly M0705)
5
1, 2, 3, 5, 9, 15, 25, 43, 73, 123, 209, 355, 601, 1019, 1729, 2931, 4969, 8427, 14289, 24227, 41081, 69659, 118113, 200275, 339593, 575819, 976369, 1655555, 2807193, 4759931, 8071041, 13685427, 23205289, 39347371, 66718225, 113128803, 191823545, 325259995
OFFSET
1,2
REFERENCES
D. E. Daykin and S. J. Tucker, Introduction to Dragon Curves. Unpublished, 1976. See links in A003229 for an earlier version.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992.
Kevin Ryde, Iterations of the Dragon Curve, see index "RQ", "BQ", and "S".
FORMULA
a(n) = A003229(n-1) + A052537(n-2).
a(n) = (1/4)*abs(A078044(n+2)).
MAPLE
A003476:=-(1+z+z**2)/(-1+z+2*z**3); # Simon Plouffe in his 1992 dissertation
MATHEMATICA
LinearRecurrence[{1, 0, 2}, {1, 2, 3}, 30] (* Harvey P. Dale, Jun 01 2020 *)
PROG
(PARI) my(P=Mod('x, 'x^3-'x^2-2)); a(n) = subst(lift(P^n), 'x, 2) >> 1; \\ Kevin Ryde, Oct 16 2021
CROSSREFS
KEYWORD
nonn,easy
STATUS
approved