A086575 a(n) = 4*(10^n - 1).

0, 36, 396, 3996, 39996, 399996, 3999996, 39999996, 399999996, 3999999996, 39999999996, 399999999996, 3999999999996, 39999999999996, 399999999999996, 3999999999999996, 39999999999999996, 399999999999999996, 3999999999999999996, 39999999999999999996, 399999999999999999996

Offset: 0

Author

Ray Chandler, Jul 22 2003

Keywords

• nonn
• easy

Comments

Original definition: a(n) = k where R(k+4) = 4.

Links

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

Crossrefs

Cf. A002275, A004086 (R(n)), A083811.

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

LinearRecurrence[{11,-10},{0,36},20] (* Harvey P. Dale, May 14 2017 *)

Formula

a(n) = 4*9*A002275(n) = 4*A002283(n).

R(a(n)) = A086578(n).

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

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

G.f.: 36*x/((1 - x)*(1 - 10*x)). (End)

E.g.f.: 4*exp(x)*(exp(9*x) - 1). - Elmo R. Oliveira, Sep 12 2024

Extensions

Edited by Jinyuan Wang, Aug 04 2021