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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 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

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