A100184 Structured octagonal anti-prism numbers.

1, 16, 64, 164, 335, 596, 966, 1464, 2109, 2920, 3916, 5116, 6539, 8204, 10130, 12336, 14841, 17664, 20824, 24340, 28231, 32516, 37214, 42344, 47925, 53976, 60516, 67564, 75139, 83260, 91946, 101216, 111089, 121584, 132720, 144516, 156991, 170164, 184054, 198680

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)*(19*n^3-15*n^2+2*n). [Corrected by Luca Colucci, Mar 01 2011]

G.f.: x*(1 + 12*x + 6*x^2)/(1 - x)^4. - Colin Barker, Jun 08 2012

a(n) = Sum_{i = 0..n-1} (n + i)*(n + 2*i). - Bruno Berselli, Feb 14 2018

E.g.f.: exp(x)*x*(6 + 42*x + 19*x^2)/6. - Stefano Spezia, Oct 11 2023

Maple

a:=n->(1/6)*(19*n^3-15*n^2+2*n): seq(a(n), n=1..33); # Muniru A Asiru, Feb 14 2018

Mathematica

Rest@ CoefficientList[Series[x (1 + 12 x + 6 x^2)/(1 - x)^4, {x, 0, 32}], x] (* Michael De Vlieger, Feb 15 2018 *)

Prog

(Magma) [(1/6)*(19*n^3-15*n^2+2*n): n in [1..40]]; // Vincenzo Librandi, Aug 18 2011
(GAP) List([1..33], n -> (1/6)*(19*n^3-15*n^2+2*n)); # Muniru A Asiru, Feb 14 2018

Crossrefs

Cf. A100185 (structured anti-prisms), A100145 (for more on structured numbers).

Sequence in context: A102860 A136264 A266103 * A304845 A190099 A316542

Adjacent sequences: A100181 A100182 A100183 * A100185 A100186 A100187

Keyword

nonn,easy

Author

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

Status

approved