A033544 Wiener number of n-hexagonal triangle.

0, 27, 210, 822, 2328, 5433, 11130, 20748, 36000, 59031, 92466, 139458, 203736, 289653, 402234, 547224, 731136, 961299, 1245906, 1594062, 2015832, 2522289, 3125562, 3838884, 4676640, 5654415, 6789042, 8098650, 9602712, 11322093, 13279098

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Named after the American chemist and physician Harry Wiener (1924-1988). - Amiram Eldar, Jun 13 2021

References

• Wai Chee Shiu, C. S. Tong and P. C. B. Lam, Wiener number of some polycyclic graphs, Graph Theory Notes of New York, Vol. 32, No. 2 (1997), pp. 10-15.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Programs

Magma

[(1/10)*n*(n+1)*(4*n^3+36*n^2+79*n+16): n in [0..30]]; // Vincenzo Librandi, Oct 20 2013

Mathematica

CoefficientList[Series[3 x (2 x^3 - 11 x^2 + 16 x + 9)/(x - 1)^6, {x, 0, 30}], x] (* Vincenzo Librandi, Oct 20 2013 *)

Formula

a(n) = (1/10)*n*(n+1)*(4*n^3+36*n^2+79*n+16).

G.f.: 3*x*(2*x^3-11*x^2+16*x+9)/(x-1)^6. [Colin Barker, Oct 30 2012]

Extensions

More terms from Vincenzo Librandi, Oct 20 2013