A100165 Structured rhombic triacontahedral numbers (vertex structure 7).

1, 32, 147, 400, 845, 1536, 2527, 3872, 5625, 7840, 10571, 13872, 17797, 22400, 27735, 33856, 40817, 48672, 57475, 67280, 78141, 90112, 103247, 117600, 133225, 150176, 168507, 188272, 209525, 232320, 256711, 282752

Offset: 1

Author

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

Keywords

• nonn
• easy

Comments

Also structured pentakis dodecahedral numbers (vertex structure 7) (cf. A100173 = alternate vertex).

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. A100164 = alternate vertex; A100145 for more on structured numbers.

Cf. A260260 (comment). [Bruno Berselli, Jul 22 2015]

Programs

Magma

[(1/6)*(54*n^3-72*n^2+24*n): n in [1..40]]; // Vincenzo Librandi, Jul 26 2011

Mathematica

Table[(3(n-1)+1)^2(3(n-1)+3)/3,{n,40}] (* Harvey P. Dale, Jan 02 2020 *)

Formula

a(n) = (1/6)*(54*n^3 - 72*n^2 + 24*n) = n*(3*n-2)^2.

From Jaume Oliver Lafont, Sep 08 2009: (Start)

a(n) = (3*(n-1) + 1)^2*(3*(n-1) + 3)/3.

G.f.: x*(1 + 28*x + 25*x^2)/(1-x)^4. (End)