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A332157
a(n) = 5*(10^(2*n+1)-1)/9 + 2*10^n.
1
7, 575, 55755, 5557555, 555575555, 55555755555, 5555557555555, 555555575555555, 55555555755555555, 5555555557555555555, 555555555575555555555, 55555555555755555555555, 5555555555557555555555555, 555555555555575555555555555, 55555555555555755555555555555, 5555555555555557555555555555555
OFFSET
0,1
FORMULA
a(n) = 5*A138148(n) + 7*10^n = A002279(2n+1) + 2*10^n.
G.f.: (7 - 202*x - 300*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
A332157 := 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( {A332157(n)=10^(n*2+1)\9*5+2*10^n}, [0..15])
(Python) def A332157(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. A332117 .. A332197 (variants with different repeated digit 1, ..., 9).
Cf. A332150 .. A332159 (variants with different middle digit 0, ..., 9).
Sequence in context: A093169 A159029 A308582 * A068616 A080810 A153405
KEYWORD
nonn,base,easy
AUTHOR
M. F. Hasler, Feb 09 2020
STATUS
approved