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%I #28 Mar 11 2020 23:14:15
%S 1,0,0,1,0,1,1,0,2,1,1,2,2,2,2,3,3,3,4,3,5,5,4,6,7,6,7,8,8,9,10,9,12,
%T 12,11,14,15,14,16,17,18,19,20,20,23,24,23,26,29,27,30,32,32,35,36,36,
%U 41,41,41,45,48,47,50,53,54
%N Expansion of 1/((1-x^3)(1-x^5)(1-x^8)(1-x^12)).
%C Number of partitions of n into parts 3, 5, 8, and 12. - _Vincenzo Librandi_, Jun 04 2014
%H Vincenzo Librandi, <a href="/A029285/b029285.txt">Table of n, a(n) for n = 0..1000</a>
%H F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and Allan Wilks, <a href="http://www.emis.de/journals/JIS/VOL10/Sloane/sloane55.html">A Slow-Growing Sequence Defined by an Unusual Recurrence</a>, J. Integer Sequences, Vol. 10 (2007), #07.1.2.
%H F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and Allan Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence [<a href="http://neilsloane.com/doc/gijs.pdf">pdf</a>, <a href="http://neilsloane.com/doc/gijs.ps">ps</a>].
%H <a href="/index/Ge#Gijswijt">Index entries for sequences related to Gijswijt's sequence</a>
%H <a href="/index/Rec#order_28">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 1, 0, 1, 0, 0, 0, 0, 0, -1, 1, -1, 0, -1, 1, -1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, -1).
%p M:= Matrix(28, (i, j)->
%p `if`(i=j-1 or j=1 and i in [3, 5, 12, 16, 23, 25], 1,
%p `if`(j=1 and i in [11, 13, 15, 17, 28], -1, 0))):
%p a:= n-> (M^(n))[1, 1]:
%p seq(a(n), n=0..70); # _Alois P. Heinz_, Jul 25 2008
%t CoefficientList[Series[1/((1-x^3)(1-x^5)(1-x^8)(1-x^12)),{x,0,80}],x] (* _Harvey P. Dale_, Mar 27 2011 *)
%o (PARI) Vec(1/((1-x^3)*(1-x^5)*(1-x^8)*(1-x^12)) + O(x^80)) \\ _Jinyuan Wang_, Mar 11 2020
%K nonn,easy
%O 0,9
%A _N. J. A. Sloane_
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