A050916 a(n) = n*5^n + 1.
1, 6, 51, 376, 2501, 15626, 93751, 546876, 3125001, 17578126, 97656251, 537109376, 2929687501, 15869140626, 85449218751, 457763671876, 2441406250001, 12969970703126, 68664550781251, 362396240234376, 1907348632812501, 10013580322265626, 52452087402343751
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (11,-35,25).
Programs
-
Magma
[ n*5^n+1: n in [0..20]]; // Vincenzo Librandi, Sep 16 2011
-
Mathematica
Table[n 5^n+1,{n,0,20}] (* or *) LinearRecurrence[{11,-35,25},{1,6,51},20] (* Harvey P. Dale, Sep 15 2011 *)
Formula
a(n) = 11*a(n-1) - 35*a(n-2) + 25*a(n-3); a(0)=1, a(1)=6, a(2)=51. - Harvey P. Dale, Sep 15 2011
G.f.: -(20*x^2-5*x+1)/((x-1)*(5*x-1)^2). - Colin Barker, Oct 14 2012
From Elmo R. Oliveira, May 03 2025: (Start)
E.g.f.: exp(x)*(1 + 5*x*exp(4*x)).
a(n) = A036291(n) + 1. (End)