login
Number of paraffins.
(Formerly M3385)
1

%I M3385 #36 Jul 14 2023 14:24:53

%S 1,4,10,22,43,76,124,190,277,388,526,694,895,1132,1408,1726,2089,2500,

%T 2962,3478,4051,4684,5380,6142,6973,7876,8854,9910,11047,12268,13576,

%U 14974,16465,18052,19738,21526

%N Number of paraffins.

%D S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, Chem. Ber. 30 (1897), 1917-1926.

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

%H S. M. Losanitsch, <a href="/A000602/a000602_1.pdf">Die Isomerie-Arten bei den Homologen der Paraffin-Reihe</a>, Chem. Ber. 30 (1897), 1917-1926. (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_04">Index entries for linear recurrences with constant coefficients</a>, signature (4, -6, 4, -1).

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

%F a(n) = 1 + 5*n/2 + n^3/2. - _Enrique Pérez Herrero_, Mar 19 2012

%p A006001:=(1+2*z**3)/(z-1)**4; # conjectured by _Simon Plouffe_ in his 1992 dissertation

%K nonn

%O 0,2

%A _N. J. A. Sloane_, _Simon Plouffe_