A016285 Expansion of 1/((1-2x)(1-4x)(1-7x)).

1, 13, 119, 953, 7167, 52185, 373423, 2646601, 18657023, 131122937, 919956687, 6448083369, 45170133919, 316325146969, 2214812883311, 15505837634057, 108549453307455, 759880532759481, 5319301168007695

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (13,-50,56).

Formula

a(n) = (2/5)*2^n - (8/3)*4^n + (49/15)*7^n. - Antonio Alberto Olivares, Feb 06 2010

a(n) = 13*a(n-1) - 50*a(n-2) + 56*a(n-3). - Vincenzo Librandi, Jun 25 2013

Mathematica

CoefficientList[Series[1 / ((1 - 2 x) (1 - 4 x) (1 - 7 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jun 25 2013 *)
LinearRecurrence[{13, -50, 56}, {1, 13, 119}, 20] (* Harvey P. Dale, Jul 26 2016 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-2*x)*(1-4*x)*(1-7*x)))); /* or */ I:=[1, 13, 119]; [n le 3 select I[n] else 13*Self(n-1)-50*Self(n-2)+56*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jun 25 2013

Crossrefs

Sequence in context: A225965 A051824 A367244 * A121086 A159969 A253512

Adjacent sequences: A016282 A016283 A016284 * A016286 A016287 A016288

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved