login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Expansion of 1/((1-x^3)(1-x^5)(1-x^8)(1-x^12)).
1

%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_