A001882 a(2n) = a(2n-1) + 2a(2n-2), a(2n+1) = a(2n) + a(2n-1), with a(1) = 2 and a(2) = 3. (Formerly M0730 N0273)

2, 3, 5, 11, 16, 38, 54, 130, 184, 444, 628, 1516, 2144, 5176, 7320, 17672, 24992, 60336, 85328, 206000, 291328, 703328, 994656, 2401312, 3395968, 8198592, 11594560, 27991744, 39586304, 95569792, 135156096, 326295680, 461451776, 1114043136, 1575494912

Offset

1,1

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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

Michael Fried et al., Problem E1738, Amer. Math. Monthly, 72 (1965), 1024-1025.

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

Index entries for linear recurrences with constant coefficients, signature (0, 4, 0, -2).

Formula

G.f.: see Maple program.

Maple

A001882:=-(-2-3*z+3*z**2+z**3)/(1-4*z**2+2*z**4); # [Simon Plouffe in his 1992 dissertation for offset 0.]

Mathematica

a[1] = 2; a[2] = 3; a[n_] := a[n] = If[EvenQ[n], a[n-1] + 2*a[n-2], a[n-1] + a[n-2]]; Table[a[n], {n, 50}] (* T. D. Noe, Aug 10 2012 *)

Prog

(PARI) x='x+O('x^50); Vec((2+3*x-3*x^2-x^3)/(1-4*x^2+2*x^4)) \\ G. C. Greubel, Aug 13 2017

Crossrefs

Cf. A161941 (bisection).

Sequence in context: A366884 A282238 A004690 * A044042 A175179 A040060

Adjacent sequences: A001879 A001880 A001881 * A001883 A001884 A001885

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Removed the attribute "conjectured" from the Plouffe g.f. R. J. Mathar, Aug 17 2009

Status

approved