A093135 Expansion of g.f. (1-8*x)/((1-x)*(1-10*x)).

1, 3, 23, 223, 2223, 22223, 222223, 2222223, 22222223, 222222223, 2222222223, 22222222223, 222222222223, 2222222222223, 22222222222223, 222222222222223, 2222222222222223, 22222222222222223, 222222222222222223, 2222222222222222223, 22222222222222222223, 222222222222222222223

Offset: 0

Author

Paul Barry, Mar 24 2004

Keywords

• nonn
• easy

Comments

Second binomial transform of 2*A001045(3*n)/3 + (-1)^n.

Partial sums of A093136.

A convex combination of 10^n and 1.

In general the second binomial transform of k*Jacobsthal(3*n)/3 + (-1)^n is 1, 1+k, 1+11*k, 1+111*k, ... This is the case for k=2.

Essentially the same as A091628 (cf. 2nd formula). - Georg Fischer, Oct 06 2018

a(n) is 3^n represented in bijective base-3 numeration. - Alois P. Heinz, Aug 26 2019

Links

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

Crossrefs

Cf. A001045, A002279, A047855, A062397, A091628, A093136.

Formula

a(n) = (2*10^n + 7)/9.

a(n) = 10*a(n-1) - 7 (with a(0)=1). - Vincenzo Librandi, Aug 02 2010

From Elmo R. Oliveira, Apr 03 2025: (Start)

E.g.f.: exp(x)*(7 + 2*exp(9*x))/9.

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

a(n) = (A062397(n) - A002279(n))/2. (End)

Extensions

More terms from Elmo R. Oliveira, Apr 03 2025