A100173 Structured pentakis dodecahedral numbers (vertex structure 6).

1, 32, 148, 404, 855, 1556, 2562, 3928, 5709, 7960, 10736, 14092, 18083, 22764, 28190, 34416, 41497, 49488, 58444, 68420, 79471, 91652, 105018, 119624, 135525, 152776, 171432, 191548, 213179, 236380, 261206, 287712

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..5000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A100165 = alternate vertex; A100145 for more on structured numbers.

Programs

Magma

[(1/6)*(55*n^3-75*n^2+26*n): n in [1..40]]; // Vincenzo Librandi, Jul 26 2011

Mathematica

LinearRecurrence[{4,-6,4,-1},{1,32,148,404},40] (* Harvey P. Dale, Aug 04 2022 *)

Formula

a(n) = (1/6)*(55*n^3 - 75*n^2 + 26*n).

G.f.: x*(1 + 28*x + 26*x^2)/(1-x)^4. - Colin Barker, May 29 2012