A029014 - OEIS

%I #18 May 14 2017 00:00:55

%S 1,1,2,2,3,4,5,6,7,9,11,13,15,17,20,23,26,29,33,37,42,46,51,56,62,68,

%T 74,81,88,96,104,112,121,130,140,150,161,172,184,196,209,222,236,250,

%U 265,281,297,314,331,349,368,387

%N Expansion of 1/((1-x)(1-x^2)(1-x^5)(1-x^9)).

%C Number of partitions of n into parts 1, 2, 5 and 9. - _Ilya Gutkovskiy_, May 13 2017

%H Vincenzo Librandi, <a href="/A029014/b029014.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1,0,1,-1,-1,1,1,-1,-1,1,0,-1,1,1,-1).

%F a(0)=1, a(1)=1, a(2)=2, a(3)=2, a(4)=3, a(5)=4, a(6)=5, a(7)=6, a(8)=7, a(9)=9, a(10)=11, a(11)=13, a(12)=15, a(13)=17, a(14)=20, a(15)=23, a(16)=26, a(n)=a(n-1)+a(n-2)-a(n-3)+a(n-5)-a(n-6)-a(n-7)+a(n-8)+ a(n-9)-a(n-10)-a(n-11)+a(n-12)-a(n-14)+a(n-15)+a(n-16)-a(n-17) [From Harvey P. Dale, Mar 03 2012]

%t CoefficientList[Series[1/((1-x)(1-x^2)(1-x^5)(1-x^9)),{x,0,60}],x] (* or *) LinearRecurrence[{1,1,-1,0,1,-1,-1,1,1,-1,-1,1,0,-1,1,1,-1},{1,1,2,2,3,4,5,6,7,9,11,13,15,17,20,23,26},60] (* _Harvey P. Dale_, Mar 03 2012 *)

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_.