A019943 Expansion of 1/((1-5*x)*(1-7*x)*(1-9*x)).

1, 21, 298, 3570, 38971, 401751, 3988468, 38583300, 366449941, 3434404281, 31873887838, 293663563830, 2690806228111, 24553315831611, 223338364450408, 2026585451393160, 18355202849805481, 166009125098571741, 1499772036736668178, 13537796780062999290

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (21,-143,315).

Formula

a(n) = (5^(n+2) - 2*7^(n+2) + 9^(n+2))/8. - R. J. Mathar, Jun 29 2013

a(0)=1, a(1)=21, a(2)=298; for n>2, a(n) = 21*a(n-1) -143*a(n-2) +315*a(n-3). - Vincenzo Librandi, Jul 03 2013

a(n) = 16*a(n-1) -63*a(n-2) +5^n. - Vincenzo Librandi, Jul 03 2013

E.g.f.: (25*exp(5*x) - 98*exp(7*x) + 81*exp(9*x))/8. - G. C. Greubel, Nov 24 2018

Maple

a:= n-> (Matrix(3, (i, j)-> `if`(i=j-1, 1, `if`(j=1, [21, -143, 315][i], 0)))^n)[1, 1]: seq(a(n), n=0..25);  # Alois P. Heinz, Jul 03 2013

Mathematica

CoefficientList[Series[1/((1-5x)(1-7x)(1-9 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 03 2013 *)
LinearRecurrence[{21, -143, 315}, {1, 21, 298}, 20] (* or *) Table[(5^(n+2) - 2*7^(n+2) + 9^(n+2))/8, {n, 0, 20}] (* G. C. Greubel, Nov 24 2018 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-5*x)*(1-7*x)*(1-9*x)))); /* or */ I:=[1, 21, 298]; [n le 3 select I[n] else 21*Self(n-1)-143*Self(n-2)+315*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 03 2013
(Magma) [(5^(n+2) - 2*7^(n+2) + 9^(n+2))/8: n in [0..20]]; // G. C. Greubel, Nov 24 2018
(PARI) vector(20, n, n--; (5^(n+2) - 2*7^(n+2) + 9^(n+2))/8) \\ G. C. Greubel, Nov 24 2018
(Sage) [(5^(n+2) - 2*7^(n+2) + 9^(n+2))/8 for n in range(20)] # G. C. Greubel, Nov 24 2018
(GAP) List([0..20], n -> (5^(n+2) - 2*7^(n+2) + 9^(n+2))/8); # G. C. Greubel, Nov 24 2018

Crossrefs

Sequence in context: A041844 A295779 A021829 * A021634 A295049 A295377

Adjacent sequences: A019940 A019941 A019942 * A019944 A019945 A019946

Keyword

nonn

Author

N. J. A. Sloane

Status

approved