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A332180
a(n) = 8*(10^(2n+1)-1)/9 - 8*10^n.
11
0, 808, 88088, 8880888, 888808888, 88888088888, 8888880888888, 888888808888888, 88888888088888888, 8888888880888888888, 888888888808888888888, 88888888888088888888888, 8888888888880888888888888, 888888888888808888888888888, 88888888888888088888888888888, 8888888888888880888888888888888
OFFSET
0,2
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.
E.g.f.: 8*exp(x)*(10*exp(99*x) - 9*exp(9*x) - 1)/9. - Stefano Spezia, Jul 13 2024
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
KEYWORD
nonn,base,easy
AUTHOR
M. F. Hasler, Feb 08 2020
STATUS
approved