A016801 Expansion of g.f. 1/((1 - 3*x)*(1 - 4*x)*(1 - 7*x)).

1, 14, 135, 1120, 8621, 63714, 460195, 3280340, 23204841, 163423414, 1147981055, 8052113160, 56430306661, 395275799114, 2767989986715, 19380181827580, 135678323522081, 949816596710814, 6648989892621175

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (14,-61,84).

Formula

a(n) = 14*a(n-1) - 61*a(n-2) + 84*a(n-3); a(0)=1, a(1)=14, a(2)=135. - Harvey P. Dale, May 10 2012

a(n) = 9*3^n/4 - 16*4^n/3 + 49*7^n/12. - R. J. Mathar, Jun 23 2013

a(n) = 11*a(n-1) - 28*a(n-2) + 3^n. - Vincenzo Librandi, Jun 26 2013

E.g.f.: exp(3*x)*(27 - 64*exp(x) + 49*exp(4*x))/12. - Stefano Spezia, Feb 08 2025

Mathematica

CoefficientList[Series[1/((1-3x)(1-4x)(1-7x)), {x, 0, 20}], x] (* or *) LinearRecurrence[{14, -61, 84}, {1, 14, 135}, 20] (* Harvey P. Dale, May 10 2012 *)

Prog

(PARI) Vec(1/((1-3*x)*(1-4*x)*(1-7*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
(Magma) I:=[1, 14, 135]; [n le 3 select I[n] else 14*Self(n-1)-61*Self(n-2)+84*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jun 26 2013
(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1/((1-3*x)*(1-4*x)*(1-7*x))))); // Vincenzo Librandi, Jun 26 2013

Crossrefs

Sequence in context: A164598 A073554 A272652 * A323857 A244651 A004004

Adjacent sequences: A016798 A016799 A016800 * A016802 A016803 A016804

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved