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

1,2

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).

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

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 *)

Prog

(Magma) [(1/6)*(13*n^3-9*n^2+2*n): n in [1..40]]; // Vincenzo Librandi, Aug 18 2011
(PARI) vector(40, n, (13*n^3 - 9*n^2 + 2*n)/6) \\ G. C. Greubel, Nov 08 2018

Crossrefs

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

Sequence in context: A372500 A249923 A340231 * A050490 A169881 A200669

Adjacent sequences: A100180 A100181 A100182 * A100184 A100185 A100186

Keyword

easy,nonn

Author

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

Status

approved