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A332123
a(n) = 2*(10^(2n+1)-1)/9 + 10^n.
4
3, 232, 22322, 2223222, 222232222, 22222322222, 2222223222222, 222222232222222, 22222222322222222, 2222222223222222222, 222222222232222222222, 22222222222322222222222, 2222222222223222222222222, 222222222222232222222222222, 22222222222222322222222222222, 2222222222222223222222222222222
OFFSET
0,1
FORMULA
a(n) = 2*A138148(n) + 3*10^n = A002276(2n+1) + 10^n.
G.f.: (3 - 101*x - 100*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
A332123 := n -> 2*(10^(2*n+1)-1)/9+10^n;
MATHEMATICA
Array[2 (10^(2 # + 1)-1)/9 + 10^# &, 15, 0]
PROG
(PARI) apply( {A332123(n)=10^(n*2+1)\9*2+10^n}, [0..15])
(Python) def A332123(n): return 10**(n*2+1)//9*2+10**n
CROSSREFS
Cf. A002275 (repunits R_n = (10^n-1)/9), A002276 (2*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. A332120 .. A332129 (variants with different middle digit 0, ..., 9).
Sequence in context: A228871 A195500 A099426 * A100201 A159807 A065580
KEYWORD
nonn,base,easy
AUTHOR
M. F. Hasler, Feb 09 2020
STATUS
approved