OFFSET
1,2
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Enrique Pérez Herrero, Table of n, a(n) for n = 1..5000
S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, Chem. Ber. 30 (1897), 1917-1926.
S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, Chem. Ber. 30 (1897), 1917-1926. (Annotated scanned copy)
Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).
FORMULA
G.f.: (x^5+2*x^4+x^3+x^2+1)/((-1+x)^2*(-1+x^2)^2).
a(n) = A005997(n) - (n-1)^2. - Enrique Pérez Herrero, Mar 28 2012
From Enrique Navarrete, Feb 22 2026: (Start)
a(n) = (1/8)*(2*n^3 - 6*n^2 + 17*n - 7 - (n+1)*(-1)^n).
E.g.f.: 1 + (1/8)*((2*x^3 + 13*x - 7)*exp(x) + (x - 1)*exp(-x)). (End)
MAPLE
A005999:=n->1+floor((n-1)/2)+2*(binomial(n+1, 3)-binomial(floor((n+1)/2), 3)-binomial(ceil((n+1)/2), 3))-(n-1)^2: seq(A005999(n), n=1..40); # Wesley Ivan Hurt, Sep 16 2014
MATHEMATICA
A005997[n_] := 1 + Floor[(n-1)/2] + 2*(Binomial[n+1, 3] -Binomial[Floor[(n+1)/2], 3] - Binomial[Ceiling[(n+1)/2], 3]); A005999[n_] := A005997[n] - (n-1)^2; Array[A005999, 100] (* Enrique Pérez Herrero, Apr 22 2012 *)
PROG
(Magma) [1+Floor((n-1)/2)+2*(Binomial(n+1, 3)-Binomial(Floor((n+1)/2), 3)-Binomial(Ceiling((n+1)/2), 3))-(n-1)^2 : n in [1..50]]; // Wesley Ivan Hurt, Sep 16 2014
(PARI) Vec( (x^5+2*x^4+x^3+x^2+1)/(-1+x)^2/(-1+x^2)^2 + O(x^66) ) \\ Joerg Arndt, Sep 16 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved