login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A005997 Number of paraffins.
(Formerly M2832)
9

%I M2832

%S 1,3,10,20,39,63,100,144,205,275,366,468,595,735,904,1088,1305,1539,

%T 1810,2100,2431,2783,3180,3600,4069,4563,5110,5684,6315,6975,7696,

%U 8448,9265,10115,11034,11988,13015,14079,15220,16400,17661,18963,20350,21780,23299

%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 Enrique Pérez Herrero, <a href="/A005997/b005997.txt">Table of n, a(n) for n = 1..5000</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1).

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

%F a(n) = A005999(n)+(n-1)^2. - _Enrique Pérez Herrero_, Mar 27 2012

%F a(n) = 1 + floor((n-1)/2) + 2*(C(n+1,3)-C(floor((n+1)/2),3)-C(ceiling((n+1)/2),3). - _Enrique Pérez Herrero_, Apr 22 2012

%F a(n) = (n+1)(2n^2-(-1)^n+1)/8. - _Bruno Berselli_, Apr 22 2012

%F a(n) = A004526(n) + 2*A111384(n). - _Enrique Pérez Herrero_, Apr 25 2012

%p a:= n-> (Matrix([[0, 0, -1, -5, -12, -26]]). Matrix(6, (i, j)-> if (i=j-1) then 1 elif j=1 then [2, 1, -4, 1, 2, -1][i] else 0 fi)^n)[1, 1]: seq (a(n), n=1..50); # _Alois P. Heinz_, Jul 31 2008

%t A005997[n_]:=1+Floor[(n-1)/2]+2*(Binomial[n+1,3]-Binomial[Floor[(n+1)/2],3]-Binomial[Ceiling[(n+1)/2],3]); Array[A005997,37] (* _Enrique Pérez Herrero_, Apr 22 2012 *)

%t LinearRecurrence[{2, 1, -4, 1, 2, -1}, {1, 3, 10, 20, 39, 63}, 37] (* _Bruno Berselli_, Apr 22 2012 *)

%Y Cf. A005999.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_.

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 10 13:27 EST 2016. Contains 279004 sequences.