|
%I #18 Sep 08 2022 08:45:15
%S 1,62,293,804,1705,3106,5117,7848,11409,15910,21461,28172,36153,45514,
%T 56365,68816,82977,98958,116869,136820,158921,183282,210013,239224,
%U 271025,305526,342837,383068,426329,472730,522381,575392
%N Structured disdyakis triacontahedral numbers (vertex structure 11).
%C Also structured deltoidal hexacontahedral numbers (vertex structure 11) (cf. A100166, A100159 = alternate vertices).
%H Vincenzo Librandi, <a href="/A100158/b100158.txt">Table of n, a(n) for n = 1..5000</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)*(110*n^3 - 150*n^2 + 46*n).
%F G.f.: x*(1 + 58*x + 51*x^2)/(1-x)^4. - _Colin Barker_, Apr 16 2012
%F E.g.f.: x*(3 + 90*x + 55*x^2)*exp(x)/3. - _G. C. Greubel_, Oct 18 2018
%t Table[(110*n^3 - 150*n^2 + 46*n)/6, {n,1,50}] (* or *) LinearRecurrence[{4,-6,4,-1}, {1, 62, 293, 804}, 50] (* _G. C. Greubel_, Oct 18 2018 *)
%o (Magma) [(1/6)*(110*n^3-150*n^2+46*n): n in [1..40]]; // _Vincenzo Librandi_, Jul 19 2011
%o (PARI) vector(50, n, (110*n^3 - 150*n^2 + 46*n)/6) \\ _G. C. Greubel_, Oct 18 2018
%Y Cf. A100159, A100160 = alternate vertices; A100145 for more on structured polyhedral numbers.
%K nonn,easy
%O 1,2
%A James A. Record (james.record(AT)gmail.com), Nov 07 2004
|
