A332187 a(n) = 8*(10^(2n+1)-1)/9 - 10^n.

7, 878, 88788, 8887888, 888878888, 88888788888, 8888887888888, 888888878888888, 88888888788888888, 8888888887888888888, 888888888878888888888, 88888888888788888888888, 8888888888887888888888888, 888888888888878888888888888, 88888888888888788888888888888, 8888888888888887888888888888888

Offset: 0

Author

M. F. Hasler, Feb 08 2020

Keywords

• nonn
• base
• easy

Links

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

Crossrefs

Cf. (A077776-1)/2 = A183190: indices of primes.

Cf. A002275 (repunits R_n = (10^n-1)/9), A002282 (8*R_n), A011557 (10^n).

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

Cf. A332117 .. A332197 (variants with different "wing" digit 1, ..., 9).

Cf. A332180 .. A332189 (variants with different middle digit 0, ..., 9).

Programs

Maple

A332187 := n -> 8*(10^(2*n+1)-1)/9-10^n;

Mathematica

Array[8 (10^(2 # + 1)-1)/9 - 10^# &, 15, 0]
LinearRecurrence[{111,-1110,1000},{7,878,88788},20] (* Harvey P. Dale, Jul 21 2024 *)

PARI

apply( {A332187(n)=10^(n*2+1)\9*8-10^n}, [0..15])

Python

def A332187(n): return 10**(n*2+1)//9*8-10**n

Formula

a(n) = 8*A138148(n) + 7*10^n = A002282(2n+1) - 10^n.

G.f.: (7 + 101*x - 900*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.