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A100185 Structured meta-anti-prism numbers, the n-th number from a structured n-gonal anti-prism 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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
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)/(1-x)^5. [Colin Barker, Jun 08 2012]
EXAMPLE
There are no 1- or 2-gonal anti-prisms, 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^4-8*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 anti-prisms; A006484 for other structured meta numbers; and A100145 for more on structured numbers.
Sequence in context: A212039 A055485 A000306 * A357251 A291888 A217324
KEYWORD
easy,nonn
AUTHOR
James A. Record (james.record(AT)gmail.com)
STATUS
approved

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Last modified April 18 13:50 EDT 2024. Contains 371780 sequences. (Running on oeis4.)