A100172 Structured triakis icosahedral numbers (vertex structure 4).

1, 32, 150, 412, 875, 1596, 2632, 4040, 5877, 8200, 11066, 14532, 18655, 23492, 29100, 35536, 42857, 51120, 60382, 70700, 82131, 94732, 108560, 123672, 140125, 157976, 177282, 198100, 220487, 244500, 270196, 297632

Offset: 1

Author

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

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A100164 = alternate vertex; A100145 for more on structured numbers.

Programs

Magma

[(1/6)*(57*n^3-81*n^2+30*n): n in [1..40]]; // Vincenzo Librandi, Jul 27 2011

Mathematica

LinearRecurrence[{4,-6,4,-1},{1,32,150,412},50] (* Harvey P. Dale, Sep 18 2023 *)

Formula

a(n) = (1/6)*(57*n^3 - 81*n^2 + 30*n).

G.f.: x*(1 + 28*x + 28*x^2)/(1-x)^4. [Colin Barker, May 29 2012]