A097362 - OEIS

%I #25 Jun 20 2017 01:35:15

%S 1,4,2,6,3,8,4,10,5,12,6,14,7,16,8,18,9,20,10,22,11,24,12,26,13,28,14,

%T 30,15,32,16,34,17,36,18,38,19,40,20,42,21,44,22,46,23,48,24,50,25,52,

%U 26,54,27,56,28,58,29,60,30,62,31,64,32,66,33,68,34,70,35,72,36,74,37

%N a(n) = (n+1)/2 if n is odd, n+2 otherwise.

%C May be regarded as table T(n,j) for j=1 to 2, where T(n,1)=n, T(n,2)=2*n+2 T(n,1)=number of carbon atoms in alkane hydrocarbons C_n H_{2n+2}, T(n,2)=number of hydrogen atoms in alkane hydrocarbons C_nH_{2n+2}.

%H Arkadiusz Wesolowski, <a href="/A097362/b097362.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-1).

%F G.f.: (2 + x)/(1 - x^2)^2. - _Arkadiusz Wesolowski_, Dec 28 2011

%t a[n_] := If[OddQ[n], (n + 1)/2, n + 2]; Table[a[n], {n, 100}] (* _Stefan Steinerberger_, May 13 2006 *)

%t LinearRecurrence[{0,2,0,-1},{1,4,2,6},100] (* _Harvey P. Dale_, Sep 14 2016 *)

%o (PARI) a(n)=if(n%2,(n+1)/2,n+2) \\ _Charles R Greathouse IV_, Sep 02 2015

%Y Cf. A065423.

%K easy,nonn

%O 1,2

%A _Pierre CAMI_, Sep 18 2004

%E More terms from _Stefan Steinerberger_, May 13 2006