A100166 Structured deltoidal hexacontahedral numbers (vertex structure 9).

1, 62, 295, 812, 1725, 3146, 5187, 7960, 11577, 16150, 21791, 28612, 36725, 46242, 57275, 69936, 84337, 100590, 118807, 139100, 161581, 186362, 213555, 243272, 275625, 310726, 348687, 389620, 433637, 480850, 531371, 585312

Offset: 1

Author

James A. Record (james.record(AT)gmail.com), Nov 07 2004

Keywords

• nonn
• easy

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. A100158, A100159 = alternate vertices; A100145 for more on structured numbers.

Programs

Magma

[(1/6)*(112*n^3-156*n^2+50*n): n in [1..40]]; // Vincenzo Librandi, Jul 26 2011

Mathematica

LinearRecurrence[{4,-6,4,-1},{1,62,295,812},40] (* Harvey P. Dale, Nov 15 2022 *)

Formula

a(n) = (1/6)*(112*n^3 - 156*n^2 + 50*n).

G.f.: x*(1 + 58*x + 53*x^2)/(1-x)^4. - Colin Barker, Jan 19 2012