A006001 Number of paraffins. (Formerly M3385)

1, 4, 10, 22, 43, 76, 124, 190, 277, 388, 526, 694, 895, 1132, 1408, 1726, 2089, 2500, 2962, 3478, 4051, 4684, 5380, 6142, 6973, 7876, 8854, 9910, 11047, 12268, 13576, 14974, 16465, 18052, 19738, 21526

Offset

0,2

References

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

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

Links

Table of n, a(n) for n=0..35.

S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, Chem. Ber. 30 (1897), 1917-1926. (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 (4, -6, 4, -1).

Formula

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

a(n) = 1 + 5*n/2 + n^3/2. - Enrique Pérez Herrero, Mar 19 2012

Maple

A006001:=(1+2*z**3)/(z-1)**4; # conjectured by Simon Plouffe in his 1992 dissertation

Crossrefs

Sequence in context: A065568 A007825 A008256 * A034357 A023626 A048574

Adjacent sequences: A005998 A005999 A006000 * A006002 A006003 A006004

Keyword

nonn

Author

N. J. A. Sloane, Simon Plouffe

Status

approved