A100183 Structured hexagonal anti-prism numbers.

1, 12, 46, 116, 235, 416, 672, 1016, 1461, 2020, 2706, 3532, 4511, 5656, 6980, 8496, 10217, 12156, 14326, 16740, 19411, 22352, 25576, 29096, 32925, 37076, 41562, 46396, 51591, 57160, 63116, 69472

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. A100185 - structured anti-prisms; A100145 for more on structured numbers.

Programs

Magma

[(1/6)*(13*n^3-9*n^2+2*n): n in [1..40]]; // Vincenzo Librandi, Aug 18 2011

Mathematica

Table[(13*n^3 - 9*n^2 + 2*n)/6, {n,1,40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 12, 46, 116}, 40] (* G. C. Greubel, Nov 08 2018 *)

PARI

vector(40, n, (13*n^3 - 9*n^2 + 2*n)/6) \\ G. C. Greubel, Nov 08 2018

Formula

a(n) = (1/6)*(13*n^3 - 9*n^2 + 2*n). [Corrected by Luca Colucci, Mar 01 2011]

G.f.: x*(1 + 8*x + 4*x^2)/(1-x)^4. - Colin Barker, Jun 08 2012

E.g.f.: (6*x +30*x^2 +13*x^3)*exp(x)/6. - G. C. Greubel, Nov 08 2018