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%I #18 Sep 08 2022 08:45:57
%S 1,34,169,478,1033,1906,3169,4894,7153,10018,13561,17854,22969,28978,
%T 35953,43966,53089,63394,74953,87838,102121,117874,135169,154078,
%U 174673,197026,221209,247294,275353,305458,337681
%N Number of partitions of 12*n into parts < 5.
%C Number of ways of placing of 12*n indistinguishable objects into indistinguishable boxes with condition that in each box can be at most 4 objects.
%H Vincenzo Librandi, <a href="/A191593/b191593.txt">Table of n, a(n) for n = 0..1000</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) = 12*n^3 + 15*n^2 + 6*n + 1.
%F From _R. J. Mathar_, Jun 08 2011: (Start)
%F a(n) = A001400(12n) = A014126(6n).
%F G.f.: (1 + 30*x + 39*x^2 + 2*x^3) / (x-1)^4. (End)
%e a(1)=34 all partitions of 1*12=12 into parts < 5 are:
%e [1,1,1,1,1,1,1,1,1,1,1,1],
%e [1,1,1,1,1,1,1,1,1,1,2],
%e [1,1,1,1,1,1,1,1,1,3],
%e [1,1,1,1,1,1,1,1,2,2],
%e [1,1,1,1,1,1,1,1,4],
%e [1,1,1,1,1,1,1,2,3],
%e [1,1,1,1,1,1,2,2,2],
%e [1,1,1,1,1,1,2,4],
%e [1,1,1,1,1,1,3,3],
%e [1,1,1,1,1,2,2,3],
%e [1,1,1,1,2,2,2,2],
%e [1,1,1,1,1,3,4],
%e [1,1,1,1,2,2,4],
%e [1,1,1,1,2,3,3],
%e [1,1,1,2,2,2,3],
%e [1,1,2,2,2,2,2],
%e [1,1,1,1,4,4],
%e [1,1,1,2,3,4],
%e [1,1,1,3,3,3],
%e [1,1,2,2,2,4],
%e [1,1,2,2,3,3],
%e [1,2,2,2,2,3],
%e [2,2,2,2,2,2],
%e [1,1,2,4,4],
%e [1,1,3,3,4],
%e [1,2,2,3,4],
%e [1,2,3,3,3],
%e [2,2,2,2,4],
%e [2,2,2,3,3],
%e [1,3,4,4],
%e [2,2,4,4],
%e [2,3,3,4],
%e [3,3,3,3],
%e [4,4,4].
%t Table[12n^3 + 15n^2 + 6n + 1, {n, 0, 30}]
%o (Magma) [12*n^3+15*n^2+6*n+1: n in [0..30]]; // _Vincenzo Librandi_, Jun 16 2011
%K nonn,easy
%O 0,2
%A _Adi Dani_, Jun 07 2011
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