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%I #20 Sep 08 2022 08:45:15
%S 1,12,44,108,215,376,602,904,1293,1780,2376,3092,3939,4928,6070,7376,
%T 8857,10524,12388,14460,16751,19272,22034,25048,28325,31876,35712,
%U 39844,44283,49040,54126,59552
%N Structured truncated tetrahedral numbers.
%H Vincenzo Librandi, <a href="/A100156/b100156.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)*(11*n^3 - 3*n^2 - 2*n).
%F From _Harvey P. Dale_, Sep 28 2011: (Start)
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(0)=1, a(1)=12, a(2)=44, a(3)=108.
%F G.f.: x*(2*x*(x+4)+1)/(x-1)^4. (End)
%F E.g.f.: x*(6 + 30*x + 11*x^2)*exp(x)/6. - _G. C. Greubel_, Oct 18 2018
%t Table[(11n^3-3n^2-2n)/6,{n,40}] (* or *) LinearRecurrence[{4,-6,4,-1},{1,12,44,108},40] (* _Harvey P. Dale_, Sep 28 2011 *)
%o (Magma) [(1/6)*(11*n^3-3*n^2-2*n): n in [1..40]]; // _Vincenzo Librandi_, Jul 19 2011
%o (PARI) vector(50, n, (11*n^3 - 3*n^2 - 2*n)/6) \\ _G. C. Greubel_, Oct 18 2018
%Y Cf. A100155, A100157 for adjacent structured Archimedean solids; A100145 for more on structured polyhedral numbers. Similar to truncated tetrahedral numbers A005906.
%K easy,nonn
%O 1,2
%A James A. Record (james.record(AT)gmail.com), Nov 07 2004
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