A100171 Structured triakis octahedral numbers (vertex structure 4).

1, 14, 60, 160, 335, 606, 994, 1520, 2205, 3070, 4136, 5424, 6955, 8750, 10830, 13216, 15929, 18990, 22420, 26240, 30471, 35134, 40250, 45840, 51925, 58526, 65664, 73360, 81635, 90510, 100006, 110144

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. A100157 = alternate vertex; A100145 for more on structured numbers.

Programs

Magma

[(1/6)*(21*n^3-27*n^2+12*n): n in [1..40]]; // Vincenzo Librandi, Jul 27 2011

Mathematica

Table[(21n^3-27n^2+12n)/6,{n,40}] (* or *) LinearRecurrence[ {4,-6,4,-1},{1,14,60,160},40] (* Harvey P. Dale, Jun 28 2011 *)

Formula

a(n)=(1/6)*(21*n^3-27*n^2+12*n).

a(0)=1, a(1)=14, a(2)=60, a(3)=160, a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - Harvey P. Dale, Jun 28 2011

G.f.: (10*x^2+10*x+1)/(x-1)^4. - Harvey P. Dale, Jun 28 2011