A332180 a(n) = 8*(10^(2n+1)-1)/9 - 8*10^n.

0, 808, 88088, 8880888, 888808888, 88888088888, 8888880888888, 888888808888888, 88888888088888888, 8888888880888888888, 888888888808888888888, 88888888888088888888888, 8888888888880888888888888, 888888888888808888888888888, 88888888888888088888888888888, 8888888888888880888888888888888

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

G.f.: 8*x*(101 - 200*x)/((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

A332180 := n -> 8*((10^(2*n+1)-1)/9-10^n);

Mathematica

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

Prog

(PARI) apply( {A332180(n)=(10^(n*2+1)\9-10^n)*8}, [0..15])
(Python) def A332180(n): return (10**(n*2+1)//9-10**n)*8

Crossrefs

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. A332120 .. A332190 (variants with different repeated digit 2, ..., 9).

Cf. A332181 .. A332189 (variants with different middle digit 1, ..., 9).

Subsequence of A006072 (numbers with mirror symmetry about middle), A153806 (strobogrammatic cyclops numbers), and A204095 (numbers whose decimal digits are in {0,8}).

Sequence in context: A252682 A235093 A259959 * A160034 A273811 A252028

Adjacent sequences: A332177 A332178 A332179 * A332181 A332182 A332183

Keyword

nonn,base,easy

Author

M. F. Hasler, Feb 08 2020

Status

approved