A100185 Structured meta-anti-prism numbers, the n-th number from a structured n-gonal anti-prism number sequence.

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

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)/(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

Adjacent sequences: A100182 A100183 A100184 * A100186 A100187 A100188

Keyword

easy,nonn

Author

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

Status

approved