A006001 Number of paraffins.

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

Author

N. J. A. Sloane, Simon Plouffe

Keywords

• nonn

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

• 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).

Programs

Maple

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

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