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A029099 Expansion of 1/((1-x)(1-x^5)(1-x^8)(1-x^12)). 0

%I #11 May 21 2017 07:27:53

%S 1,1,1,1,1,2,2,2,3,3,4,4,5,6,6,7,8,9,10,10,12,13,14,15,17,19,20,21,23,

%T 25,27,28,31,33,35,37,40,43,45,47,51,54,57,59,63,67,70,73,78,82,86,89,

%U 94,99,103,107,113,118,123

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

%C Number of partitions of n into parts 1, 5, 8 and 12. - _Ilya Gutkovskiy_, May 21 2017

%H <a href="/index/Rec#order_26">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, -2, 1, 0, 0, -1, 1, 0, -1, 1, 0, 0, 0, 1, -1).

%F a(0)=1, a(1)=1, a(2)=1, a(3)=1, a(4)=1, a(5)=2, a(6)=2, a(7)=2, a(8)=3, a(9)=3, a(10)=4, a(11)=4, a(12)=5, a(13)=6, a(14)=6, a(15)=7, a(16)=8, a(17)=9, a(18)=10, a(19)=10, a(20)=12, a(21)=13, a(22)=14, a(23)=15, a(24)=17, a(25)=19, a(n)=a(n-1)+a(n-5)-a(n-6)+a(n-8)-a(n-9)+a(n-12)-2*a(n-13)+a(n-14)-a(n-17)+a(n-18)-a(n-20)+a(n-21)+a(n-25)-a(n-26). - _Harvey P. Dale_, Oct 18 2012

%t CoefficientList[Series[1/((1-x)(1-x^5)(1-x^8)(1-x^12)),{x,0,60}],x] (* or *) LinearRecurrence[{1,0,0,0,1,-1,0,1,-1,0,0,1,-2,1,0,0,-1,1,0,-1,1,0,0,0,1,-1},{1,1,1,1,1,2,2,2,3,3,4,4,5,6,6,7,8,9,10,10,12,13,14,15,17,19},70] (* _Harvey P. Dale_, Oct 18 2012 *)

%K nonn

%O 0,6

%A _N. J. A. Sloane_.

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Last modified March 28 14:21 EDT 2024. Contains 371254 sequences. (Running on oeis4.)