A020000 Expansion of 1/((1-5*x)*(1-7*x)*(1-11*x)).

1, 23, 362, 4870, 60411, 715533, 8243572, 93366380, 1046230421, 11644889443, 129058033182, 1426436938290, 15738640474831, 173461105001753, 1910430676985192, 21031277618176600, 231459987587209641

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (23,-167,385)

Programs

Magma

m:=20; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-5*x)*(1-7*x)*(1-11*x)))); // Vincenzo Librandi, Jul 03 2013

Magma

I:=[1, 23, 362]; [n le 3 select I[n] else 23*Self(n-1)-167*Self(n-2)+385*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 03 2013

Mathematica

CoefficientList[Series[1 / ((1 - 5 x) (1 - 7 x) (1 - 11 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 03 2013 *)
LinearRecurrence[{23,-167,385},{1,23,362},20] (* Harvey P. Dale, May 09 2025 *)

PARI

Vec(1/((1-5*x)*(1-7*x)*(1-11*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Formula

a(n) = 5^(n+2)/12+11^(n+2)/24-7^(n+2)/8. - R. J. Mathar, Mar 15 2011

a(0)=1, a(1)=23, a(2)=362; for n>2, a(n) = 23*a(n-1) -167*a(n-2) +385*a(n-3). - Vincenzo Librandi, Jul 03 2013

a(n) = 18*a(n-1) -77*a(n-2) +5^n. - Vincenzo Librandi, Jul 03 2013