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%I #21 Sep 08 2022 08:45:15
%S 1,12,46,116,235,416,672,1016,1461,2020,2706,3532,4511,5656,6980,8496,
%T 10217,12156,14326,16740,19411,22352,25576,29096,32925,37076,41562,
%U 46396,51591,57160,63116,69472
%N Structured hexagonal anti-prism numbers.
%H Vincenzo Librandi, <a href="/A100183/b100183.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = (1/6)*(13*n^3 - 9*n^2 + 2*n). [Corrected by _Luca Colucci_, Mar 01 2011]
%F G.f.: x*(1 + 8*x + 4*x^2)/(1-x)^4. - _Colin Barker_, Jun 08 2012
%F E.g.f.: (6*x +30*x^2 +13*x^3)*exp(x)/6. - _G. C. Greubel_, Nov 08 2018
%t 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 *)
%o (Magma) [(1/6)*(13*n^3-9*n^2+2*n): n in [1..40]]; // _Vincenzo Librandi_, Aug 18 2011
%o (PARI) vector(40, n, (13*n^3 - 9*n^2 + 2*n)/6) \\ _G. C. Greubel_, Nov 08 2018
%Y Cf. A100185 - structured anti-prisms; A100145 for more on structured numbers.
%K easy,nonn
%O 1,2
%A James A. Record (james.record(AT)gmail.com), Nov 07 2004
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