PROG
(MAGMAMagma) [12*n^3+15*n^2+6*n+1: n in [0..30]]; // Vincenzo Librandi, Jun 16 2011
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(MAGMAMagma) [12*n^3+15*n^2+6*n+1: n in [0..30]]; // Vincenzo Librandi, Jun 16 2011
proposed
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editing
proposed
Number of partitions of 12*n into parts < 5.
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.
a(n) = 12*n^3 + 15*n^2 + 6*n + 1.
From R. J. Mathar, Jun 08 2011: (Start)
a(n) = A001400(12n) = A014126(6n).
a(n) = A001400(12n) = A014126(6n). G.f. : (1 + 30*x + 39*x^2 + 2*x^3) / (x-1)^4 . - R. J. Mathar, Jun 08 2011(End)
a(1)=34 all partitions of 1*12=12 into parts < 5 are:
(MAGMA) [12*n^3+15*n^2+6*n+1: n in [0..30]]; // _Vincenzo Librandi, _, Jun 16 2011
approved
editing
<a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
<a href="/index/Rec">Index to sequences with entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1)
<a href="/index/Rea#recLCCRec">Index to sequences with linear recurrences with constant coefficients</a>, signature (4,-6,4,-1)
_Adi Dani (inadida(AT)yahoo.com), _, Jun 07 2011
<a href="/Sindx_index/Rea.html#recLCC">Index to sequences with linear recurrences with constant coefficients</a>, signature (4,-6,4,-1)
proposed
approved