A179558 a(1)=10; a(n) = a(n-1)*10 - 5^(n-2).

10, 99, 985, 9825, 98125, 980625, 9803125, 98015625, 980078125, 9800390625, 98001953125, 980009765625, 9800048828125, 98000244140625, 980001220703125, 9800006103515625, 98000030517578125, 980000152587890625, 9800000762939453125, 98000003814697265625

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

Cf. A000351, A011557.

Sequence in context: A242633 A004189 A322054 * A179556 A179477 A179555

Adjacent sequences: A179555 A179556 A179557 * A179559 A179560 A179561

Keyword

nonn,easy

Author

Mark Dols, Jul 19 2010

Status

approved