A100170 Structured pentagonal hexacontahedral numbers (vertex structure 10).

1, 92, 444, 1228, 2615, 4776, 7882, 12104, 17613, 24580, 33176, 43572, 55939, 70448, 87270, 106576, 128537, 153324, 181108, 212060, 246351, 284152, 325634, 370968, 420325, 473876, 531792, 594244, 661403, 733440, 810526, 892832

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. A100169 = alternate vertex; A100145 for more on structured numbers.

Programs

Magma

[(1/6)*(171*n^3-243*n^2+78*n): n in [1..40]]; // Vincenzo Librandi, Jul 27 2011

PARI

a(n)=n*(171*n^2-243*n+78)/6 \\ Charles R Greathouse IV, Feb 06 2012

Formula

a(n) = (1/6)*(171*n^3 - 243*n^2 + 78*n).

G.f.: x*(1 + 88*x + 82*x^2)/(1-x)^4. - Colin Barker, Feb 14 2012