A332189 a(n) = 8*(10^(2n+1)-1)/9 + 10^n.

9, 898, 88988, 8889888, 888898888, 88888988888, 8888889888888, 888888898888888, 88888888988888888, 8888888889888888888, 888888888898888888888, 88888888888988888888888, 8888888888889888888888888, 888888888888898888888888888, 88888888888888988888888888888, 8888888888888889888888888888888

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) + 9*10^n = A002282(2n+1) + 10^n.

G.f.: (9 - 101*x - 700*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.

Maple

A332189 := n -> 8*(10^(2*n+1)-1)/9+10^n;

Mathematica

Array[8 (10^(2 # + 1)-1)/9 + 10^# &, 15, 0]

Prog

(PARI) apply( {A332189(n)=10^(n*2+1)\9*8+10^n}, [0..15])
(Python) def A332189(n): return 10**(n*2+1)//9*8+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. A332119 .. A332189 (variants with different "wing" digit 1, ..., 8).

Cf. A332180 .. A332187 (variants with different middle digit 0, ..., 7).

Sequence in context: A225169 A287034 A027878 * A045793 A069054 A283801

Adjacent sequences: A332186 A332187 A332188 * A332190 A332191 A332192

Keyword

nonn,base,easy

Author

M. F. Hasler, Feb 08 2020

Status

approved