A159941 - OEIS

%I #19 Dec 01 2021 12:33:43

%S 8,32,92,212,416,728,1172,1772,2552,3536,4748,6212,7952,9992,12356,

%T 15068,18152,21632,25532,29876,34688,39992,45812,52172,59096,66608,

%U 74732,83492,92912,103016,113828,125372,137672

%N Number of trisubstituted linear alkanes of composition C_n H_(2n-1) XYZ.

%C See the paper by Valentin Vankov Iliev for details.

%H V. V. Iliev, <a href="http://dx.doi.org/10.1007/s10910-009-9534-4">A mathematical characterization of the groups of substitution isomerism of the linear alkanes</a>, J. Math. Chem. 47 (2010), p 52-61.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F a(n) = (4*n^3 - 18*n^2 + 38*n - 28) where n is the number of carbons.

%F a(n) = 2*A159940(n). - _R. J. Mathar_, Jul 08 2009

%F G.f.: 4*x^2*(2+3*x^2+x^3)/(1-x)^4. - _Colin Barker_, Aug 07 2012

%F a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - _Wesley Ivan Hurt_, May 28 2021

%e The number of trisubstituted linear decane (n = 10) is 2552.

%Y Cf. A002522, A033816, A159938, A159940.

%K nonn,easy

%O 2,1

%A _Parthasarathy Nambi_, Apr 26 2009