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

%I #36 Sep 08 2022 08:44:43

%S 1,17,202,2090,20251,189707,1745332,15900020,144066901,1301455397,

%T 11737424062,105758621150,952437144751,8574983669087,77190104636392,

%U 694787214149480,6253466332501801,56283104147438777,506557473488982322,4559064943373269010

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

%H Vincenzo Librandi, <a href="/A017897/b017897.txt">Table of n, a(n) for n = 0..200</a>

%H Christian Brouder, William J. Keith, Ângela Mestre, <a href="http://arxiv.org/abs/1301.0874">Closed forms for a multigraph enumeration</a>, arXiv preprint arXiv:1301.0874 [math.CO], 2013-2015.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (17,-87,135).

%F 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

%F 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

%F a(n) = 14*a(n-1) - 45*a(n-2) + 3^n. - _Vincenzo Librandi_, Jul 01 2013

%F a(n) = (9^(n+2) - 3*5^(n+2) + 2*3^(n+2))/24. - _Yahia Kahloune_, Aug 13 2013

%p 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

%t CoefficientList[Series[1 / ((1 - 3 x) (1 - 5 x) (1 - 9 x)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Jul 01 2013 *)

%t LinearRecurrence[{17,-87,135},{1,17,202},30] (* _Harvey P. Dale_, Sep 26 2014 *)

%t a[n_]:=(9^(n+2) - 3*5^(n+2) + 2*3^(n+2))/24; Array[a, 30, 0] (* _Stefano Spezia_, Oct 04 2018 *)

%o (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

%o (PARI) a(n) = (9^(n+2) - 3*5^(n+2) + 2*3^(n+2))/24; \\ _Joerg Arndt_, Aug 13 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

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Last modified March 29 06:44 EDT 2024. Contains 371265 sequences. (Running on oeis4.)