A332186 a(n) = 8*(10^(2n+1)-1)/9 - 2*10^n.

6, 868, 88688, 8886888, 888868888, 88888688888, 8888886888888, 888888868888888, 88888888688888888, 8888888886888888888, 888888888868888888888, 88888888888688888888888, 8888888888886888888888888, 888888888888868888888888888, 88888888888888688888888888888, 8888888888888886888888888888888

Offset

0,1

Links

Table of n, a(n) for n=0..15.

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

Formula

a(n) = 8*A138148(n) + 6*10^n = A002282(2n+1) - 2*10^n = 2*A332143(n).

G.f.: (6 + 202*x - 1000*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.

E.g.f.: 2*exp(x)*(40*exp(99*x) - 9*exp(9*x) - 4)/9. - Stefano Spezia, Jul 13 2024

Maple

A332186 := n -> 8*(10^(2*n+1)-1)/9-2*10^n;

Mathematica

Array[8 (10^(2 # + 1)-1)/9 - 2*10^# &, 15, 0]
LinearRecurrence[{111, -1110, 1000}, {6, 868, 88688}, 20] (*or *) Table[FromDigits[Join[PadRight[ {}, n, 8], PadRight[ {6}, n+1, 8]]], {n, 0, 20}] (* Harvey P. Dale, May 30 2023 *)

Prog

(PARI) apply( {A332186(n)=10^(n*2+1)\9*8-2*10^n}, [0..15])
(Python) def A332186(n): return 10**(n*2+1)//9*8-2*10**n

Crossrefs

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

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

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

Sequence in context: A201141 A078927 A064430 * A279304 A180992 A229629

Adjacent sequences: A332183 A332184 A332185 * A332187 A332188 A332189

Keyword

nonn,base,easy

Author

M. F. Hasler, Feb 08 2020

Status

approved