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%I #20 Sep 08 2022 08:45:15
%S 1,24,100,260,535,956,1554,2360,3405,4720,6336,8284,10595,13300,16430,
%T 20016,24089,28680,33820,39540,45871,52844,60490,68840,77925,87776,
%U 98424,109900,122235,135460,149606,164704
%N Structured truncated cubic numbers.
%H Vincenzo Librandi, <a href="/A100152/b100152.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)*n*(31*n^2 - 27*n + 2).
%F G.f.: x*(1 + 20*x + 10*x^2)/(1-x)^4. - _Colin Barker_, Jan 19 2012
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(1)=1, a(2)=24, a(3)=100, a(4)=260. - _Harvey P. Dale_, Jan 11 2016
%F E.g.f.: x*(6 + 66*x + 31*x^2)*exp(x)/6. - _G. C. Greubel_, Oct 18 2018
%t Table[n/6 (31n^2-27n+2),{n,40}] (* or *) LinearRecurrence[{4,-6,4,-1},{1,24,100,260},40] (* _Harvey P. Dale_, Jan 11 2016 *)
%o (Magma) [(1/6)*(31*n^3-27*n^2+2*n): n in [1..40]]; // _Vincenzo Librandi_, Jul 19 2011
%o (PARI) vector(50, n, (31*n^3-27*n^2+2*n)/6) \\ _G. C. Greubel_, Oct 18 2018
%Y Cf. A100151, A100153 for adjacent structured Archimedean solids; A100145 for more on structured polyhedral numbers. Similar to truncated cubic numbers A005912.
%K nonn,easy
%O 1,2
%A James A. Record (james.record(AT)gmail.com), Nov 07 2004
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