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A100184 Structured octagonal anti-prism 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 (list; graph; refs; listen; history; text; internal format)
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

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

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Last modified November 30 00:02 EST 2022. Contains 358431 sequences. (Running on oeis4.)