A332121 a(n) = 2*(10^(2n+1)-1)/9 - 10^n.

1, 212, 22122, 2221222, 222212222, 22222122222, 2222221222222, 222222212222222, 22222222122222222, 2222222221222222222, 222222222212222222222, 22222222222122222222222, 2222222222221222222222222, 222222222222212222222222222, 22222222222222122222222222222, 2222222222222221222222222222222

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

Cf. A332131 .. A332191 (variants with different repeated digit 3, ..., 9).

Programs

Maple

A332121 := n -> 2*(10^(2*n+1)-1)/9-10^n;

Mathematica

Array[2 (10^(2 # + 1)-1)/9 - 10^# &, 15, 0]

PARI

apply( {A332121(n)=10^(n*2+1)\9*2-10^n}, [0..15])

Python

def A332121(n): return 10**(n*2+1)//9*2-10**n

Formula

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

G.f.: (1 + 101*x - 300*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.