A016299 Expansion of 1/((1-2*x)*(1-5*x)*(1-10*x)).

1, 17, 209, 2293, 23961, 244797, 2473969, 24869813, 249349001, 2496744877, 24983724129, 249918620133, 2499593099641, 24997965496157, 249989827476689, 2499949137375253, 24999745686859881, 249998728434266637

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..100

Index entries for linear recurrences with constant coefficients, signature (17,-80,100).

Formula

a(n) = 17*a(n-1) - 80*a(n-2) + 100*a(n-3); a(0)=1, a(1)=17, a(2)=209. - Harvey P. Dale, Aug 24 2011

a(n) = 15*a(n-1) - 50*a(n-2) + 2^n; a(0)=1, a(1)=17. - Vincenzo Librandi, Aug 25 2011

a(n) = (1/6)*(2^n - 10*5^n + 15*10^n). - Bruno Berselli, Aug 25 2011

Mathematica

CoefficientList[Series[1/((1-2x)(1-5x)(1-10x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{17, -80, 100}, {1, 17, 209}, 30] (* Harvey P. Dale, Aug 24 2011 *)

Prog

(Magma) [ n eq 1 select 1 else n eq 2 select 17 else n eq 3 select 209 else 17*Self(n-1)-80*Self(n-2) +100*Self(n-3): n in [1..20] ]; // Vincenzo Librandi, Aug 25 2011
(Magma) /*By definition*/ m:=18; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-2*x)*(1-5*x)*(1-10*x)))); // Bruno Berselli, Aug 25 2011
(PARI) Vec(1/((1-2*x)*(1-5*x)*(1-10*x))+O(x^18)) \\ Bruno Berselli, Aug 25 2011

Crossrefs

Sequence in context: A239157 A014921 A081035 * A016250 A255819 A070137

Adjacent sequences: A016296 A016297 A016298 * A016300 A016301 A016302

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved