A029133 - OEIS

%I #13 Jul 30 2015 23:08:50

%S 1,1,1,1,1,1,1,1,1,2,3,3,4,4,4,4,4,4,5,6,7,8,9,9,10,10,10,11,12,13,15,

%T 16,17,18,19,19,21,22,23,25,27,28,30,31,32,34,36,37,40,42,44,46,48,49,

%U 52,54,56,59,62,64,68,70

%N Expansion of 1/((1-x)(1-x^9)(1-x^10)(1-x^12)).

%C Number of partitions of n into parts 1, 9, 10, and 12. [_Joerg Arndt_, Mar 10 2014]

%H Vincenzo Librandi, <a href="/A029133/b029133.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_32">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 1, -1, 0, 0, 0, 0, 0, -1, 1, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, -1).

%F a(0)=1, a(1)=1, a(2)=1, a(3)=1, a(4)=1, a(5)=1, a(6)=1, a(7)=1, a(8)=1, a(9)=2, a(10)=3, a(11)=3, a(12)=4, a(13)=4, a(14)=4, a(15)=4, a(16)=4, a(17)=4, a(18)=5, a(19)=6, a(20)=7, a(21)=8, a(22)=9, a(23)=9, a(24)=10, a(25)=10, a(26)=10, a(27)=11, a(28)=12, a(29)=13, a(30)=15, a(31)=16, a(n)=a(n-1)+a(n-9)-a(n-11)+a(n-12)-a(n-13)- a(n-19)+ a(n-20)- a(n-21)+ a(n-23)+ a(n-31)-a(n-32). - _Harvey P. Dale_, Mar 08 2014

%t CoefficientList[Series[1/((1 - x) (1 - x^9) (1 - x^10) (1 - x^12)), {x, 0, 70}], x] (* _Harvey P. Dale_, Mar 08 2014 *)

%t LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 1, -1, 0, 0, 0, 0, 0, -1, 1, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, -1}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 4, 4, 4, 4, 4, 4, 5, 6, 7, 8, 9, 9, 10, 10, 10, 11, 12, 13, 15, 16}, 70] (* _Harvey P. Dale_, Mar 08 2014 *)

%K nonn

%O 0,10

%A _N. J. A. Sloane_.