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A332158
a(n) = 5*(10^(2*n+1)-1)/9 + 3*10^n.
1
8, 585, 55855, 5558555, 555585555, 55555855555, 5555558555555, 555555585555555, 55555555855555555, 5555555558555555555, 555555555585555555555, 55555555555855555555555, 5555555555558555555555555, 555555555555585555555555555, 55555555555555855555555555555, 5555555555555558555555555555555
OFFSET
0,1
FORMULA
a(n) = 5*A138148(n) + 8*10^n = A002279(2n+1) + 3*10^n.
G.f.: (8 - 303*x - 200*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
A332158 := n -> 5*(10^(2*n+1)-1)/9+3*10^n;
MATHEMATICA
Array[5 (10^(2 # + 1)-1)/9 + 3*10^# &, 15, 0]
PROG
(PARI) apply( {A332158(n)=10^(n*2+1)\9*5+3*10^n}, [0..15])
(Python) def A332158(n): return 10**(n*2+1)//9*5+3*10**n
CROSSREFS
Cf. A002275 (repunits R_n = (10^n-1)/9), A002279 (5*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
Cf. A332118 .. A332178, A181965 (variants with different repeated digit 1, ..., 9).
Cf. A332150 .. A332159 (variants with different middle digit 0, ..., 9).
Sequence in context: A188780 A015023 A225168 * A269508 A090923 A336941
KEYWORD
nonn,base,easy
AUTHOR
M. F. Hasler, Feb 09 2020
STATUS
approved