A050917 a(n) = n*6^n + 1.
1, 7, 73, 649, 5185, 38881, 279937, 1959553, 13436929, 90699265, 604661761, 3990767617, 26121388033, 169789022209, 1097098297345, 7052774768641, 45137758519297, 287753210560513, 1828079220031489, 11577835060199425, 73123168801259521, 460675963447934977
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (13,-48,36).
Programs
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Magma
[ n*6^n+1: n in [0..20]]; // Vincenzo Librandi, Sep 16 2011
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Mathematica
Table[n 6^n+1,{n,0,40}] (* or *) LinearRecurrence[{13,-48,36},{1,7,73},40] (* Harvey P. Dale, Feb 20 2013 *) -
PARI
vector(20, n, n--; n*6^n + 1) \\ Michel Marcus, Jun 11 2015
Formula
G.f.: -(30*x^2-6*x+1)/((x-1)*(6*x-1)^2). - Colin Barker, Oct 14 2012
a(n) = 13*a(n-1) - 48*a(n-2) + 36*a(n-3); a(0)=1, a(1)=7, a(2)=73. - Harvey P. Dale, Feb 20 2013
From Elmo R. Oliveira, May 03 2025: (Start)
E.g.f.: exp(x)*(1 + 6*x*exp(5*x)).
a(n) = A036292(n) + 1. (End)