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A001584
A generalized Fibonacci sequence.
(Formerly M0235 N0080)
1
1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 4, 4, 4, 7, 7, 8, 12, 12, 16, 21, 21, 31, 37, 38, 58, 65, 71, 106, 114, 135, 191, 201, 257, 341, 359, 485, 605, 652, 904, 1070, 1202, 1664, 1894, 2237, 3029, 3370, 4176, 5464, 6048, 7779, 9793, 10963, 14411, 17492, 20054, 26507, 31239, 36924, 48396
OFFSET
0,9
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
V. C. Harris and C. C. Styles, Generalized Fibonacci sequences associated with a generalized Pascal triangle, Fib. Quart., 4 (1966), 241-248.
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
FORMULA
G.f.: (1 + x + x^2 - x^3 - x^4 - x^5)/(1 - 2*x^3 + x^6 - x^8).
MAPLE
A001584:=(z-1)*(z**2+z+1)**2/(z**4-z**3+1)/(z**4+z**3-1); # Simon Plouffe in his 1992 dissertation
PROG
(PARI) Vec((1+x+x^2-x^3-x^4-x^5)/(1-2*x^3+x^6-x^8) + O(x^80)) \\ Michel Marcus, Sep 07 2017
CROSSREFS
Cf. A017817.
Sequence in context: A218084 A240046 A363947 * A180019 A274496 A112801
KEYWORD
nonn,easy
EXTENSIONS
More terms from David W. Wilson
STATUS
approved