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A332153
a(n) = 5*(10^(2*n+1)-1)/9 - 2*10^n.
1
3, 535, 55355, 5553555, 555535555, 55555355555, 5555553555555, 555555535555555, 55555555355555555, 5555555553555555555, 555555555535555555555, 55555555555355555555555, 5555555555553555555555555, 555555555555535555555555555, 55555555555555355555555555555, 5555555555555553555555555555555
OFFSET
0,1
FORMULA
a(n) = 5*A138148(n) + 3*10^n = A002279(2n+1) - 2*10^n.
G.f.: (3 + 202*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
A332153 := n -> 5*(10^(2*n+1)-1)/9-2*10^n;
MATHEMATICA
Array[5 (10^(2 # + 1)-1)/9 - 2*10^# &, 15, 0]
PROG
(PARI) apply( {A332153(n)=10^(n*2+1)\9*5-2*10^n}, [0..15])
(Python) def A332153(n): return 10**(n*2+1)//9*5-2*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. A332113 .. A332193 (variants with different repeated digit 1, ..., 9).
Cf. A332150 .. A332159 (variants with different middle digit 0, ..., 9).
Sequence in context: A133026 A100339 A195626 * A158247 A034314 A265459
KEYWORD
nonn,base,easy
AUTHOR
M. F. Hasler, Feb 09 2020
STATUS
approved