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%I #7 Jul 31 2015 12:49:40
%S 1,2,3,5,8,11,17,23,31,41,54,68,88,109,135,165,202,241,291,344,407,
%T 477,559,646,751,862,990,1129,1288,1456,1651,1857,2089,2338,2617,2911,
%U 3244,3594,3982,4395,4851,5330,5862,6420,7031,7677,8382,9120,9929,10775
%N The sixth column of triangle A091492, excluding leading zeros.
%C Excluding leading zeros, columns k=3,4,5, of triangle A091492 list the partitions of n into k parts.
%C This sequence is related to the partitions of n into at most 6 parts (A001402) since A(x)=(1+x-x^5)*G001402(x), where G001402(x) is the g.f. for A001402.
%H <a href="/index/Rec#order_21">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, 0, 0, -1, 0, -2, 0, 1, 1, 1, 1, 0, -2, 0, -1, 0, 0, 1, 1, -1).
%F G.f.: (1+x-x^5)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)*(1-x^6))
%F a(0)=1, a(1)=2, a(2)=3, a(3)=5, a(4)=8, a(5)=11, a(6)=17, a(7)=23, a(8)=31, a(9)=41, a(10)=54, a(11)=68, a(12)=88, a(13)=109, a(14)=135, a(15)=165, a(16)=202, a(17)=241, a(18)=291, a(19)=344, a(20)=407, a(n)=a(n-1)+ a(n-2)- a(n-5)-2*a(n-7)+a(n-9)+a(n-10)+a(n-11)+a(n-12)-2*a(n-14)-a(n-16)+ a(n-19)+ a(n-20)-a (n-21). - _Harvey P. Dale_, Dec 09 2012
%t CoefficientList[Series[(1+x-x^5)/((1-x)(1-x^2)(1-x^3)(1-x^4)(1-x^5)(1-x^6)),{x,0,60}],x] (* or *) LinearRecurrence[ {1,1,0,0,-1,0,-2,0,1,1,1,1,0,-2,0,-1,0,0,1,1,-1},{1,2,3,5,8,11,17,23,31,41,54,68,88,109,135,165,202,241,291,344,407},60](* _Harvey P. Dale_, Dec 09 2012 *)
%o (PARI) {a(n)=polcoeff( (1+x-x^5)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)*(1-x^6)) +O(x^(n+1)),n,x)}
%Y Cf. A091492, A091493, A001402.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jan 16 2004
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