OFFSET
1,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..200
Index entries for linear recurrences with constant coefficients, signature (17,-31,15).
FORMULA
a(n) = 17*a(n-1) - 31*a(n-2) + 15*a(n-3); a(1)=1, a(2)=17, a(3)=258. - Vincenzo Librandi, Oct 20 2012
From Elmo R. Oliveira, Mar 29 2025: (Start)
G.f.: x/((1-15*x)*(1-x)^2).
E.g.f.: exp(x)*(15*exp(14*x) - 14*x - 15)/196.
a(n) = (15^(n+1) - 14*n - 15)/196. (End)
MATHEMATICA
LinearRecurrence[{17, -31, 15}, {1, 17, 258}, 20] (* Vincenzo Librandi, Oct 20 2012 *)
nxt[{n_, a_}]:={n+1, 15a+n+1}; NestList[nxt, {1, 1}, 20][[;; , 2]] (* Harvey P. Dale, Jun 15 2025 *)
PROG
(Magma) I:=[1, 17, 258]; [n le 3 select I[n] else 17*Self(n-1) - 31*Self(n-2) + 15*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Oct 20 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved