A159941 Number of trisubstituted linear alkanes of composition C_n H_(2n-1) XYZ.

8, 32, 92, 212, 416, 728, 1172, 1772, 2552, 3536, 4748, 6212, 7952, 9992, 12356, 15068, 18152, 21632, 25532, 29876, 34688, 39992, 45812, 52172, 59096, 66608, 74732, 83492, 92912, 103016, 113828, 125372, 137672

Offset: 2

Author

Parthasarathy Nambi, Apr 26 2009

Keywords

• nonn
• easy

Comments

See the paper by Valentin Vankov Iliev for details.

Examples

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

Links

• V. V. Iliev, A mathematical characterization of the groups of substitution isomerism of the linear alkanes, J. Math. Chem. 47 (2010), p 52-61.
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A002522, A033816, A159938, A159940.

Formula

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

a(n) = 2*A159940(n). - R. J. Mathar, Jul 08 2009

G.f.: 4*x^2*(2+3*x^2+x^3)/(1-x)^4. - Colin Barker, Aug 07 2012

a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - Wesley Ivan Hurt, May 28 2021