A021714 Expansion of 1/((1-x)(1-3x)(1-10x)(1-11x)).
1, 25, 428, 6278, 84879, 1092243, 13601506, 165488176, 1979095877, 23357343581, 272803757304, 3159571375194, 36342586372795, 415641464948839, 4730786270092622, 53625950549096132, 605758471885400433
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (25,-197,503,-330).
Programs
-
Magma
m:=20; R
:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-10*x)*(1-11*x)))); // Bruno Berselli, May 07 2013 -
Mathematica
CoefficientList[Series[1/((1 - x) (1 - 3 x) (1 - 10 x) (1 - 11 x)), {x, 0, 20}], x] (* Bruno Berselli, May 07 2013 *) LinearRecurrence[{25,-197,503,-330},{1,25,428,6278},20] (* Harvey P. Dale, Jan 16 2024 *) -
PARI
Vec(1/((1-x)*(1-3*x)*(1-10*x)*(1-11*x))+O(x^20)) \\ Bruno Berselli, May 07 2013
Formula
G.f.: 1/((1-x)*(1-3*x)*(1-10*x)*(1-11*x)).
a(n) = -1/180 +3^(n+3)/112 -10^(n+3)/63 +11^(n+3)/80. [Bruno Berselli, May 07 2013]
a(n)-11*a(n-1) = A016215(n). [Bruno Berselli, May 08 2013]