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 A100183 Structured hexagonal anti-prism numbers. 1
 1, 12, 46, 116, 235, 416, 672, 1016, 1461, 2020, 2706, 3532, 4511, 5656, 6980, 8496, 10217, 12156, 14326, 16740, 19411, 22352, 25576, 29096, 32925, 37076, 41562, 46396, 51591, 57160, 63116, 69472 (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 (4,-6,4,-1). FORMULA a(n) = (1/6)*(13*n^3 - 9*n^2 + 2*n). [Corrected by Luca Colucci, Mar 01 2011] G.f.: x*(1 + 8*x + 4*x^2)/(1-x)^4. - Colin Barker, Jun 08 2012 E.g.f.: (6*x +30*x^2 +13*x^3)*exp(x)/6. - G. C. Greubel, Nov 08 2018 MATHEMATICA Table[(13*n^3 - 9*n^2 + 2*n)/6, {n, 1, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 12, 46, 116}, 40] (* G. C. Greubel, Nov 08 2018 *) PROG (MAGMA) [(1/6)*(13*n^3-9*n^2+2*n): n in [1..40]]; // Vincenzo Librandi, Aug 18 2011 (PARI) vector(40, n, (13*n^3 - 9*n^2 + 2*n)/6) \\ G. C. Greubel, Nov 08 2018 CROSSREFS Cf. A100185 - structured anti-prisms; A100145 for more on structured numbers. Sequence in context: A199211 A331764 A249923 * A050490 A169881 A200669 Adjacent sequences:  A100180 A100181 A100182 * A100184 A100185 A100186 KEYWORD easy,nonn AUTHOR James A. Record (james.record(AT)gmail.com), Nov 07 2004 STATUS approved

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Last modified March 30 11:16 EDT 2020. Contains 333125 sequences. (Running on oeis4.)