A086576 a(n) = 5*(10^n - 1).

0, 45, 495, 4995, 49995, 499995, 4999995, 49999995, 499999995, 4999999995, 49999999995, 499999999995, 4999999999995, 49999999999995, 499999999999995, 4999999999999995, 49999999999999995, 499999999999999995, 4999999999999999995, 49999999999999999995, 499999999999999999995

Offset: 0

Author

Ray Chandler, Jul 22 2003

Keywords

• nonn
• base
• easy

Comments

Original definition: a(n) = k where R(k+5) = 5.

Examples

			From _John Elias_, Jun 23 2021: (Start)
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45;
11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99 = 495;
111 + 222 + 333 + 444 + 555 + 666 + 777 + 888 + 999 = 4995;
1111 + 2222 + 3333 + 4444 + 5555 + 6666 + 7777 + 8888 + 9999 = 49995;
11111 + 22222 + 33333 + 44444 + 55555 + 66666 + 77777 + 88888 + 99999 = 499995; etc. (End)
		

Links

• Index entries for linear recurrences with constant coefficients, signature (11,-10).

Crossrefs

Cf. A002275, A004086 (R(n)).

Cf. One of family of sequences of form a(n)=k, where R(k+m)=m, m = 1 to 9; m=1: A002283, m=2: A086573, m=3: A086574, m=4: A086575, m=5: A086576, m=6: A086577, m=7: A086578, m=8: A086579, m=9: A086580.

Programs

Mathematica

Join[{0}, LinearRecurrence[{11,-10},{45,495},50]] (* G. C. Greubel, Jul 08 2016 *)

Formula

a(n) = 5*9*A002275(n) = 5*A002283(n).

R(a(n)) = A086577(n).

From Chai Wah Wu, Jul 08 2016: (Start)

a(n) = 11*a(n-1) - 10*a(n-2) for n > 1.

G.f.: 45*x/((1 - x)*(1 - 10*x)). (End)

E.g.f.: 5*exp(x)*(exp(9*x) - 1). - Elmo R. Oliveira, Sep 12 2024

Extensions

Name edited by Jinyuan Wang, Aug 04 2021