

A100185


Structured metaantiprism numbers, the nth number from a structured ngonal antiprism number sequence.


9



1, 4, 19, 68, 185, 416, 819, 1464, 2433, 3820, 5731, 8284, 11609, 15848, 21155, 27696, 35649, 45204, 56563, 69940, 85561, 103664, 124499, 148328, 175425, 206076, 240579, 279244, 322393, 370360, 423491, 482144
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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 (5,10,10,5,1).


FORMULA

a(n) = (1/6)*(3*n^4  8*n^3 + 9*n^2 + 2*n).
G.f.: x*(1  x + 9*x^2 + 3*x^3)/(1x)^5. [Colin Barker, Jun 08 2012]


EXAMPLE

There are no 1 or 2gonal antiprisms, so 1 and (2n) are used as the first and second terms since all the sequences begin as such.


PROG

(MAGMA) [(1/6)*(3*n^48*n^3+9*n^2+2*n): n in [1..40]]; // Vincenzo Librandi, Aug 03 2011


CROSSREFS

Cf. A005900, A000447, A096000, A100178, A100157, A100185  structured antiprisms; A006484 for other structured meta numbers; and A100145 for more on structured numbers.
Sequence in context: A212039 A055485 A000306 * A291888 A217324 A129019
Adjacent sequences: A100182 A100183 A100184 * A100186 A100187 A100188


KEYWORD

easy,nonn


AUTHOR

James A. Record (james.record(AT)gmail.com)


STATUS

approved



