

A100184


Structured octagonal antiprism numbers.


1



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
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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^315*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..n1} (n + i)*(n + 2*i).  Bruno Berselli, Feb 14 2018


MAPLE

a:=n>(1/6)*(19*n^315*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^315*n^2+2*n): n in [1..40]]; // Vincenzo Librandi, Aug 18 2011
(GAP) List([1..33], n > (1/6)*(19*n^315*n^2+2*n)); # Muniru A Asiru, Feb 14 2018


CROSSREFS

Cf. A100185 (structured antiprisms), 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



