A100167 Structured pentagonal icositetrahedral numbers (vertex structure 13).

1, 38, 171, 460, 965, 1746, 2863, 4376, 6345, 8830, 11891, 15588, 19981, 25130, 31095, 37936, 45713, 54486, 64315, 75260, 87381, 100738, 115391, 131400, 148825, 167726, 188163, 210196, 233885, 259290, 286471, 315488

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. A100168 = alternate vertex; A100145 for more on structured numbers.

Programs

Magma

[(1/6)*(60*n^3-72*n^2+18*n): n in [1..40]]; // Vincenzo Librandi, Jul 26 2011

Mathematica

Table[(60n^3-72n^2+18n)/6,{n,40}] (* or *) LinearRecurrence[{4,-6,4,-1},{1,38,171,460},40] (* Harvey P. Dale, Aug 21 2016 *)

Formula

a(n) = (1/6)*(60*n^3 - 72*n^2 + 18*n).

G.f.: x*(1 + 34*x + 25*x^2)/(1-x)^4. - Colin Barker, Feb 14 2012