A332181 a(n) = 8*(10^(2n+1)-1)/9 - 7*10^n.

1, 818, 88188, 8881888, 888818888, 88888188888, 8888881888888, 888888818888888, 88888888188888888, 8888888881888888888, 888888888818888888888, 88888888888188888888888, 8888888888881888888888888, 888888888888818888888888888, 88888888888888188888888888888, 8888888888888881888888888888888

Offset

0,2

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

G.f.: (1 + 707*x - 1500*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

A332181 := n -> 8*(10^(2*n+1)-1)/9-7*10^n;

Mathematica

Array[8 (10^(2 # + 1)-1)/9 - 7*10^# &, 15, 0]

Prog

(PARI) apply( {A332181(n)=10^(n*2+1)\9*8-7*10^n}, [0..15])
(Python) def A332181(n): return 10**(n*2+1)//9*8-7*10**n

Crossrefs

Cf. (A077776-1)/2 = A183184: 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).

Cf. A332121 .. A332191 (variants with different repeated digit 2, ..., 9).

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

Sequence in context: A279441 A221748 A105989 * A266059 A356414 A020445

Adjacent sequences: A332178 A332179 A332180 * A332182 A332183 A332184

Keyword

nonn,base,easy

Author

M. F. Hasler, Feb 08 2020

Status

approved