A001584 A generalized Fibonacci sequence. (Formerly M0235 N0080)

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

T. D. Noe, Table of n, a(n) for n = 0..1000

V. C. Harris and C. C. Styles, Generalized Fibonacci sequences associated with a generalized Pascal triangle, Fib. Quart., 4 (1966), 241-248.

V. C. Harris and C. C. Styles, Generalized Fibonacci sequences associated with a generalized Pascal triangle and accompanying letter (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

Index entries for linear recurrences with constant coefficients, signature (0, 0, 2, 0, 0, -1, 0, 1).

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

Adjacent sequences: A001581 A001582 A001583 * A001585 A001586 A001587

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from David W. Wilson

Status

approved