A017897 Expansion of 1/((1-3x)(1-5x)(1-9x)).

1, 17, 202, 2090, 20251, 189707, 1745332, 15900020, 144066901, 1301455397, 11737424062, 105758621150, 952437144751, 8574983669087, 77190104636392, 694787214149480, 6253466332501801, 56283104147438777, 506557473488982322, 4559064943373269010

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Christian Brouder, William J. Keith, Ângela Mestre, Closed forms for a multigraph enumeration, arXiv preprint arXiv:1301.0874 [math.CO], 2013-2015.

Index entries for linear recurrences with constant coefficients, signature (17,-87,135).

Formula

a(n) = term (1,1) in the 3 X 3 matrix [17,1,0; -87,0,1; 135,0,0]^n. - Alois P. Heinz, Aug 04 2008

a(n) = 17*a(n-1) - 87*a(n-2) + 135*a(n-3); a(0)=1, a(1)=17, a(2)=202. - Vincenzo Librandi, Jul 01 2013

a(n) = 14*a(n-1) - 45*a(n-2) + 3^n. - Vincenzo Librandi, Jul 01 2013

a(n) = (9^(n+2) - 3*5^(n+2) + 2*3^(n+2))/24. - Yahia Kahloune, Aug 13 2013

Maple

a:= n -> (Matrix(3, (i, j)-> if (i=j-1) then 1 elif j=1 then [17, -87, 135][i] else 0 fi)^n)[1, 1]: seq (a(n), n=0..25); # Alois P. Heinz, Aug 04 2008

Mathematica

CoefficientList[Series[1 / ((1 - 3 x) (1 - 5 x) (1 - 9 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Jul 01 2013 *)
LinearRecurrence[{17, -87, 135}, {1, 17, 202}, 30] (* Harvey P. Dale, Sep 26 2014 *)
a[n_]:=(9^(n+2) - 3*5^(n+2) + 2*3^(n+2))/24; Array[a, 30, 0] (* Stefano Spezia, Oct 04 2018 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-5*x)*(1-9*x)))); /* or */ I:=[1, 17, 202]; [n le 3 select I[n] else 17*Self(n-1)-87*Self(n-2)+135*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 01 2013
(PARI) a(n) = (9^(n+2) - 3*5^(n+2) + 2*3^(n+2))/24; \\ Joerg Arndt, Aug 13 2013

Crossrefs

Sequence in context: A065895 A009479 A279448 * A016311 A140961 A016306

Adjacent sequences: A017894 A017895 A017896 * A017898 A017899 A017900

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved