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.
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
Keywords
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).
Crossrefs
Cf. A161941 (bisection).
Programs
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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.]
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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 *) -
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
Formula
G.f.: see Maple program.
Extensions
Removed the attribute "conjectured" from the Plouffe g.f. R. J. Mathar, Aug 17 2009