A005593 a(n) = (F(2n+1) + F(2n-1) + F(n+3) - 2)/2, where F() = Fibonacci numbers A000045.

2, 5, 12, 29, 71, 177, 448, 1147, 2960, 7679, 19989, 52145, 136214, 356121, 931540, 2437513, 6379403, 16698113, 43710756, 114427391, 299560472, 784236315, 2053119817, 5375076769, 14072035466, 36840908237, 96450492828, 252510252437

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• M. D. McIlroy, The number of states of a dynamic storage system, Computer J., 25 (No. 3, 1982), 388-392.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• M. D. McIlroy, The number of states of a dynamic storage system, Computer J., 25 (No. 3, 1982), 388-392. (Annotated scanned copy)
• 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

Programs

Maple

A005593:=-(-2+5*z-z**2-2*z**3+z**4)/(z-1)/(z**2+z-1)/(z**2-3*z+1); # conjectured by Simon Plouffe in his 1992 dissertation

Mathematica

Map[(Fibonacci[2#1+1]+Fibonacci[2#1-1]+Fibonacci[ #1+3]-2)/2&, Range[50]]

Extensions

More terms from Gabriel Cunningham (gcasey(AT)mit.edu), Oct 25 2004