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%I #20 Sep 08 2022 08:45:15
%S 1,60,285,784,1665,3036,5005,7680,11169,15580,21021,27600,35425,44604,
%T 55245,67456,81345,97020,114589,134160,155841,179740,205965,234624,
%U 265825,299676,336285,375760,418209,463740,512461,564480
%N Structured small rhombicosidodecahedral numbers.
%H Vincenzo Librandi, <a href="/A100148/b100148.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)*(108*n^3 - 150*n^2 + 48*n).
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(1)=1, a(2)=60, a(3)=285, a(4)=784. - _Harvey P. Dale_, Oct 10 2011
%F G.f.: x*(x*(51*x+56)+1)/(x-1)^4. - _Harvey P. Dale_, Oct 10 2011
%F E.g.f.: x*(1 + 29*x + 18*x^2)*exp(x). - _G. C. Greubel_, Oct 18 2018
%t Table[(108n^3-150n^2+48n)/6,{n,40}] (* or *) LinearRecurrence[ {4,-6,4,-1},{1,60,285,784},40](* _Harvey P. Dale_, Oct 10 2011 *)
%o (Magma) [(1/6)*(108*n^3-150*n^2+48*n): n in [1..40]]; // _Vincenzo Librandi_, Jul 19 2011
%o (PARI) vector(50, n, (108*n^3 - 150*n^2 + 48*n)/6) \\ _G. C. Greubel_, Oct 18 2018
%Y Cf. A100147, A100149 for adjacent structured Archimedean solids; and A100145 for more on structured polyhedral numbers.
%K easy,nonn
%O 1,2
%A James A. Record (james.record(AT)gmail.com), Nov 07 2004
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