login
A100183
Structured hexagonal anti-prism numbers.
1
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
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
KEYWORD
easy,nonn
AUTHOR
James A. Record (james.record(AT)gmail.com), Nov 07 2004
STATUS
approved