A003476 a(n) = a(n-1) + 2*a(n-3). (Formerly M0705)

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 Unpublished, 1976.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

T. D. Noe, Table of n, a(n) for n = 1..500

D. E. Daykin, Letter to N. J. A. Sloane, Mar 1974.

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".

Index entries for linear recurrences with constant coefficients, signature (1,0,2).

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

Cf. A003229, A052537, A078044.

Sequence in context: A326024 A200047 A147877 * A017989 A017990 A228646

Adjacent sequences: A003473 A003474 A003475 * A003477 A003478 A003479

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved