A100169 Structured pentagonal hexacontahedral numbers (vertex structure 16).

1, 92, 438, 1204, 2555, 4656, 7672, 11768, 17109, 23860, 32186, 42252, 54223, 68264, 84540, 103216, 124457, 148428, 175294, 205220, 238371, 274912, 315008, 358824, 406525, 458276, 514242, 574588, 639479, 709080, 783556, 863072

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. A100170 = alternate vertex; A100145 for more on structured numbers.

Programs

Magma

[(1/6)*(165*n^3-225*n^2+66*n): n in [1..40]]; // Vincenzo Librandi, Jul 27 2011

Maple

A100169:=n->(55*n^3-75*n^2+22*n)/2; seq(A100169(n), n=1..100); # Wesley Ivan Hurt, Nov 26 2013

Mathematica

Table[(55n^3 - 75n^2 + 22n)/2, {n, 100}] (* Wesley Ivan Hurt, Nov 26 2013 *)

Formula

a(n) = (1/6)*(165*n^3 - 225*n^2 + 66*n).

G.f.: x*(1 + 88*x + 76*x^2)/(1-x)^4. - Colin Barker, Feb 14 2012

a(n) = (55*n^3 - 75*n^2 + 22*n)/2. - Wesley Ivan Hurt, Nov 26 2013