A332124 a(n) = 2*(10^(2n+1)-1)/9 + 2*10^n.

4, 242, 22422, 2224222, 222242222, 22222422222, 2222224222222, 222222242222222, 22222222422222222, 2222222224222222222, 222222222242222222222, 22222222222422222222222, 2222222222224222222222222, 222222222222242222222222222, 22222222222222422222222222222, 2222222222222224222222222222222

Offset: 0

Author

M. F. Hasler, Feb 09 2020

Keywords

• nonn
• base
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002276 (2*R_n), A011557 (10^n).

Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).

Cf. A332114 .. A332194 (variants with different repeated digit 1, ..., 9).

Cf. A332120 .. A332129 (variants with different middle digit 0, ..., 9).

Programs

Maple

A332124 := n -> 2*((10^(2*n+1)-1)/9+10^n);

Mathematica

Array[2 ((10^(2 # + 1)-1)/9 + 10^#) &, 15, 0]
Table[FromDigits[Join[PadRight[{},n,2],{4},PadRight[{},n,2]]],{n,0,20}] (* or *) LinearRecurrence[{111,-1110,1000},{4,242,22422},20](* Harvey P. Dale, Mar 06 2023 *)

PARI

apply( {A332124(n)=(10^(n*2+1)\9+10^n)*2}, [0..15])

Python

def A332124(n): return (10**(n*2+1)//9+10**n)*2

Formula

a(n) = 2*A138148(n) + 4*10^n = A002276(2n+1) + 2*10^n = 2*A332112(n).

G.f.: (4 - 202*x)/((1 - x)(1 - 10*x)(1 - 100*x)).

a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.