A014929 a(1)=1, a(n) = n*14^(n-1) + a(n-1).

1, 29, 617, 11593, 203673, 3430617, 56137369, 899445401, 14181546905, 220792014745, 3402593219481, 51997375255449, 789018236134297, 11901025061692313, 178581127445062553, 2667670656370058137, 39692877399129367449, 588537118527090893721, 8699235348529189004185

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Index entries for linear recurrences with constant coefficients, signature (29,-224,196).

Formula

From R. J. Mathar, Mar 05 2008: (Start)

a(n) = (1 + (13*n - 1)*14^n)/169.

O.g.f.: x/((14*x-1)^2*(1-x)). (End)

From Elmo R. Oliveira, May 16 2025: (Start)

E.g.f.: exp(x)*(1 + exp(13*x)*(182*x - 1))/169.

a(n) = 28*a(n-1) - 196*a(n-2) + 1 for n > 2.

a(n) = 29*a(n-1) - 224*a(n-2) + 196*a(n-3) for n > 3. (End)

Maple

A014929 := proc(n) (1+(13*n-1)*14^n)/169 ; end: seq(A014929(n), n=1..10) ; # R. J. Mathar, Mar 05 2008

Mathematica

Table[(1+(13n-1)*14^n)/169, {n, 20}] (* Wesley Ivan Hurt, Feb 26 2014 *)

Prog

(Magma) [(1+(13*n-1)*14^n)/169: n in [1..20]]; // Vincenzo Librandi, Mar 04 2014
(PARI) a(n) = (1+(13*n-1)*14^n)/169; \\ Jinyuan Wang, Mar 11 2020

Crossrefs

Sequence in context: A142521 A032630 A361930 * A006136 A199038 A182329

Adjacent sequences: A014926 A014927 A014928 * A014930 A014931 A014932

Keyword

nonn,easy

Author

Olivier Gérard

Extensions

More terms from Vincenzo Librandi, Mar 04 2014

Status

approved