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

Author

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

Keywords

• easy
• nonn

Examples

			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.
		

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).

Crossrefs

Cf. A005900, A000447, A096000, A100178, A100157, A100185 - structured anti-prisms; A006484 for other structured meta numbers; and A100145 for more on structured numbers.

Programs

Magma

[(1/6)*(3*n^4-8*n^3+9*n^2+2*n): n in [1..40]]; // Vincenzo Librandi, Aug 03 2011

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]