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
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..200
- Index entries for linear recurrences with constant coefficients, signature (29,-224,196).
Programs
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Magma
[(1+(13*n-1)*14^n)/169: n in [1..20]]; // Vincenzo Librandi, Mar 04 2014
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Maple
A014929 := proc(n) (1+(13*n-1)*14^n)/169 ; end: seq(A014929(n),n=1..10) ; # R. J. Mathar, Mar 05 2008
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Mathematica
Table[(1+(13n-1)*14^n)/169, {n, 20}] (* Wesley Ivan Hurt, Feb 26 2014 *) -
PARI
a(n) = (1+(13*n-1)*14^n)/169; \\ Jinyuan Wang, Mar 11 2020
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)
Extensions
More terms from Vincenzo Librandi, Mar 04 2014