A014920 a(1)=1, a(n) = n*7^(n-1) + a(n-1).

1, 15, 162, 1534, 13539, 114381, 937924, 7526268, 59409477, 462945547, 3570173286, 27298094202, 207234827815, 1563680973513, 11737027066248, 87698011225336, 652657830908553, 4840007082678279, 35779865442976810

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (15, -63, 49).

Formula

a(1)=1, a(2)=15, a(n) = 14*a(n-1) - 49*a(n-2) + 1. - Vincenzo Librandi, Oct 23 2012

G.f.: x/((1-x)*(1-7*x)^2). - Vincenzo Librandi, Oct 23 2012

a(n) = (1/36)*(1 + 7^n*(6*n-1)). - Vincenzo Librandi, Oct 26 2012

a(1)=1, a(2)=15, a(3)=162, a(n) = 15*a(n-1) - 63*a(n-2) + 49*a(n-3). - Harvey P. Dale, Jun 26 2013

Maple

a:=n->sum (7^n-7^j, j=0..n): seq(a(n)/6, n=1..21); # Zerinvary Lajos, Dec 14 2008

Mathematica

CoefficientList[Series[1/((1 - x)(1 - 7*x)^2), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 23 2012 *)
LinearRecurrence[{15, -63, 49}, {1, 15, 162}, 30] (* Harvey P. Dale, Jun 26 2013 *)

Prog

(Magma) I:=[1, 15]; [n le 2 select I[n] else 14*Self(n-1)-49*Self(n-2)+1: n in [1..30]]; // Vincenzo Librandi, Oct 23 2012
(Magma) [(1/36)*(1+7^n*(6*n-1)): n in [1..20]]; // Vincenzo Librandi, Oct 26 2012

Crossrefs

Sequence in context: A263514 A323292 A067361 * A081034 A279157 A016243

Adjacent sequences: A014917 A014918 A014919 * A014921 A014922 A014923

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved