A029016 - OEIS

%I #21 Jun 23 2017 03:26:10

%S 1,1,2,2,3,4,5,6,7,8,10,11,14,15,18,20,23,26,29,32,36,39,44,47,53,57,

%T 63,68,74,80,87,93,101,107,116,123,133,141,151,160,171,181,193,203,

%U 216,227,241,253,268,281,297,311

%N Expansion of 1/((1-x)(1-x^2)(1-x^5)(1-x^12)).

%C Number of partitions of n into parts 1, 2, 5, and 12. - _Joerg Arndt_, May 20 2014

%H Vincenzo Librandi, <a href="/A029016/b029016.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, -1, 0, 1, -1, -1, 1, 0, 0, 0, 1, -1, -1, 1, 0, -1, 1, 1, -1).

%p M := Matrix(20, (i,j)-> if (i=j-1) or (j=1 and member(i, [1,2,5,8,12,15,18,19])) then 1 elif j=1 and member(i, [3,6,7,13,14,17,20]) then -1 else 0 fi); a := n -> (M^(n))[1,1]; seq (a(n), n=0..51); # _Alois P. Heinz_, Jul 25 2008

%t s = 1/((1-x)(1-x^2)(1-x^5)(1-x^12)) + O[x]^100; CoefficientList[s, x] (* _Jean-François Alcover_, Nov 05 2015 *)

%t LinearRecurrence[{1,1,-1,0,1,-1,-1,1,0,0,0,1,-1,-1,1,0,-1,1,1,-1},{1,1,2,2,3,4,5,6,7,8,10,11,14,15,18,20,23,26,29,32},80] (* _Harvey P. Dale_, Jun 22 2017 *)

%o (PARI) a(n)=floor((2*n^3+60*n^2+513*n+1773)/1440+(n+1)*(-1)^n/96+[0,-1,0,1,0,2][n%6+1]*(-1)^(n\6)/6) \\ _Tani Akinari_, May 19 2014

%K nonn

%O 0,3

%A _N. J. A. Sloane_