OFFSET
1,1
LINKS
Colin Barker, Table of n, a(n) for n = 1..999
Index entries for linear recurrences with constant coefficients, signature (15,-50).
FORMULA
From Colin Barker, Oct 03 2015: (Start)
a(n) = 15*a(n-1) - 50*a(n-2) for n > 2.
G.f.: -x*(51*x - 10)/((5*x - 1)*(10*x - 1)). (End)
E.g.f.: (49*exp(10*x) + 2*exp(5*x) - 51)/50. - Stefano Spezia, Mar 02 2023
MATHEMATICA
a[1] := 10; a[n_] := a[n] = 10 a[n - 1] - 5^(n - 2); Array[a@ # &, {20}] (* Michael De Vlieger, Oct 03 2015 *)
nxt[{n_, a_}] := {n + 1, 10*a - 5^(n - 1)}; NestList[nxt, {1, 10}, 20][[All, 2]] (* or *) LinearRecurrence[{15, -50}, {10, 99}, 20] (* Harvey P. Dale, Aug 01 2020 *)
PROG
(PARI) Vec(-x*(51*x-10)/((5*x-1)*(10*x-1)) + O(x^30)) \\ Colin Barker, Oct 03 2015
(PARI) a(n) = if(n<2, 10, a(n-1)*10 - 5^(n-2));
vector(30, n, a(n)) \\ Altug Alkan, Oct 03 2015
(PARI) a(n) = my(t=5^(n-2)); (49*t)<<(n-1) + t; \\ Kevin Ryde, Mar 02 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mark Dols, Jul 19 2010
STATUS
approved