OFFSET
1,2
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..1000
Daniel C. Fielder, Special integer sequences controlled by three parameters, Fibonacci Quarterly 6, 1968, 64-70.
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
Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
Index entries for linear recurrences with constant coefficients, signature (1, 1, 0, 1, 1).
FORMULA
G.f.: x(1+2x+4x^3+5x^4)/(1-x-x^2-x^4-x^5).
MAPLE
A001642:=-(z+1)*(5*z**3-z**2+z+1)/(-1+z+z**2+z**4+z**5); # conjectured by Simon Plouffe in his 1992 dissertation
MATHEMATICA
LinearRecurrence[{1, 1, 0, 1, 1}, {1, 3, 4, 11, 21}, 50] (* T. D. Noe, Aug 09 2012 *)
PROG
(PARI) a(n)=if(n<0, 0, polcoeff(x*(1+2*x+4*x^3+5*x^4)/(1-x-x^2-x^4-x^5)+x*O(x^n), n))
(Magma) I:=[1, 3, 4, 11, 21]; [n le 5 select I[n] else Self(n-1) + Self(n-2) + Self(n-4) + Self(n-5): n in [1..30]]; // G. C. Greubel, Jan 09 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved