A001584 - OEIS

%I M0235 N0080 #42 Jun 25 2023 02:35:27

%S 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,

%T 106,114,135,191,201,257,341,359,485,605,652,904,1070,1202,1664,1894,

%U 2237,3029,3370,4176,5464,6048,7779,9793,10963,14411,17492,20054,26507,31239,36924,48396

%N A generalized Fibonacci sequence.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A001584/b001584.txt">Table of n, a(n) for n = 0..1000</a>

%H V. C. Harris and C. C. Styles, <a href="http://www.fq.math.ca/Scanned/4-3/harris.pdf">Generalized Fibonacci sequences associated with a generalized Pascal triangle</a>, Fib. Quart., 4 (1966), 241-248.

%H V. C. Harris and C. C. Styles, <a href="/A001584/a001584.pdf">Generalized Fibonacci sequences associated with a generalized Pascal triangle and accompanying letter</a> (annotated scanned copy)

%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 2, 0, 0, -1, 0, 1).

%F G.f.: (1 + x + x^2 - x^3 - x^4 - x^5)/(1 - 2*x^3 + x^6 - x^8).

%p A001584:=(z-1)*(z**2+z+1)**2/(z**4-z**3+1)/(z**4+z**3-1); # _Simon Plouffe_ in his 1992 dissertation

%o (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

%Y Cf. A017817.

%K nonn,easy

%O 0,9

%A _N. J. A. Sloane_

%E More terms from _David W. Wilson_