|
%I #18 May 14 2017 05:57:40
%S 1,1,2,2,3,4,5,6,7,8,10,12,14,16,18,21,24,27,30,33,37,41,46,50,55,60,
%T 66,72,78,84,91,98,106,114,122,131,140,150,160,170,181,192,204,216,
%U 229,242,256,270,285,300,316,332,349,366,384,403,422,442,462,483
%N Expansion of 1/((1-x)(1-x^2)(1-x^5)(1-x^11)).
%C Number of partitions of n into parts 1, 2, 5 and 11. - _Ilya Gutkovskiy_, May 14 2017
%H <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1,0,1,-1,-1,1,0,0,1,-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)=8, a(10)=10, a(11)=12, a(12)=14, a(13)=16, a(14)=18, a(15)=21, a(16)=24, a(17)=27, a(18)=30, 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-11) - a(n-12) - a(n-13) + a(n-14) - a(n-16) + a(n-17) + a(n-18) - a(n-19). - _Harvey P. Dale_, Dec 24 2011
%F a(n) = floor((2*n^3 + 57*n^2 + 466*n + 1622)/1320 + (-1)^n/16). - _Tani Akinari_, May 19 2014
%p M := Matrix(19, (i,j)-> if (i=j-1) or (j=1 and member(i, [1,2,5,8,11,14,17,18])) then 1 elif j=1 and member(i, [3,6,7,12,13,16,19]) then -1 else 0 fi); a := n -> (M^(n))[1,1]; seq (a(n), n=0..51); # _Alois P. Heinz_, Jul 25 2008
%t CoefficientList[Series[1/((1-x)(1-x^2)(1-x^5)(1-x^11)),{x,0,60}],x] (* _Harvey P. Dale_, Dec 24 2011 *)
%o (PARI) a(n)=floor((2*n^3+57*n^2+466*n+1622)/1320+(-1)^n/16) \\ _Tani Akinari_, May 19 2014
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Dec 11 1999
|
