A332129 a(n) = 2*(10^(2n+1)-1)/9 + 7*10^n.

9, 292, 22922, 2229222, 222292222, 22222922222, 2222229222222, 222222292222222, 22222222922222222, 2222222229222222222, 222222222292222222222, 22222222222922222222222, 2222222222229222222222222, 222222222222292222222222222, 22222222222222922222222222222, 2222222222222229222222222222222

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. A332119 .. A332189 (variants with different repeated digit 1, ..., 8).

Cf. A332120 .. A332128 (variants with different middle digit 0, ..., 8).

Programs

Maple

A332129 := n -> 2*(10^(2*n+1)-1)/9+7*10^n;

Mathematica

Array[2 (10^(2 # + 1)-1)/9 + 7*10^# &, 15, 0]
LinearRecurrence[{111,-1110,1000},{9,292,22922},20] (* Harvey P. Dale, Jun 25 2020 *)

PARI

apply( {A332129(n)=10^(n*2+1)\9*2+7*10^n}, [0..15])

Python

def A332129(n): return 10**(n*2+1)//9*2+7*10**n

Formula

a(n) = 2*A138148(n) + 9*10^n = A002276(2n+1) + 7*10^n.

G.f.: (9 - 707*x + 500*x^2)/((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.