A205084 a(n) = n 4's sandwiched between two 1's.

11, 141, 1441, 14441, 144441, 1444441, 14444441, 144444441, 1444444441, 14444444441, 144444444441, 1444444444441, 14444444444441, 144444444444441, 1444444444444441, 14444444444444441, 144444444444444441, 1444444444444444441, 14444444444444444441

Offset: 0

Author

José María Grau Ribas, Jan 22 2012

Keywords

• nonn
• easy
• base
• less

Links

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

Crossrefs

Cf. A002278.

Programs

Mathematica

a[0]=11;a[n_]:=a[n-1]*10+31;Table[a[n],{n,0,44}]

PARI

a(n)=(130*10^n-31)/9 \\ Charles R Greathouse IV, Jan 23 2012

Formula

a(0)=11, a(n) = 10*a(n-1) + 31.

a(n) = (130*10^n - 31)/9 (see PARI's code by Charles R Greathouse IV).

From Elmo R. Oliveira, Feb 18 2025: (Start)

G.f.: (11 + 20*x)/((1 - x)*(1 - 10*x)).

E.g.f.: exp(x)*(130*exp(9*x) - 31)/9.

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