A100161 Structured disdyakis dodecahedral numbers (vertex structure 9).

1, 26, 115, 308, 645, 1166, 1911, 2920, 4233, 5890, 7931, 10396, 13325, 16758, 20735, 25296, 30481, 36330, 42883, 50180, 58261, 67166, 76935, 87608, 99225, 111826, 125451, 140140, 155933, 172870, 190991, 210336

Offset: 1

Author

James A. Record (james.record(AT)gmail.com), Nov 07 2004

Keywords

• nonn
• easy

Comments

Also structured deltoidal icositetrahedral numbers (vertex structure 9) (cf. A100162 = alternate vertex).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..5000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A100162, A100163 = alternate vertices; A100145 for more on structured polyhedral numbers.

Programs

Magma

[(1/6)*(40*n^3-48*n^2+14*n): n in [1..40]]; // Vincenzo Librandi, Jul 24 2011

Mathematica

Table[(40n^3-48n^2+14n)/6,{n,40}] (* or *) LinearRecurrence[{4,-6,4,-1},{1,26,115,308},40] (* Harvey P. Dale, Sep 23 2016 *)

Formula

a(n) = (1/6)*(40*n^3 - 48*n^2 + 14*n).

G.f.: x*(1 + 22*x + 17*x^2)/(1-x)^4. - Colin Barker, Jan 19 2012