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A332143
a(n) = 4*(10^(2*n+1)-1)/9 - 10^n.
2
3, 434, 44344, 4443444, 444434444, 44444344444, 4444443444444, 444444434444444, 44444444344444444, 4444444443444444444, 444444444434444444444, 44444444444344444444444, 4444444444443444444444444, 444444444444434444444444444, 44444444444444344444444444444, 4444444444444443444444444444444
OFFSET
0,1
FORMULA
a(n) = 4*A138148(n) + 3*10^n = A002278(2n+1) - 10^n.
G.f.: (3 + 101*x - 500*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
A332143 := n -> 4*(10^(2*n+1)-1)/9-10^n;
MATHEMATICA
Array[4 (10^(2 # + 1)-1)/9 - 10^# &, 15, 0]
PROG
(PARI) apply( {A332143(n)=10^(n*2+1)\9*4-10^n}, [0..15])
(Python) def A332143(n): return 10**(n*2+1)//9*4-10**n
CROSSREFS
Cf. A002275 (repunits R_n = (10^n-1)/9), A002278 (4*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. A332140 .. A332149 (variants with different middle digit 0, ..., 9).
Sequence in context: A229751 A172859 A087771 * A277234 A269553 A361886
KEYWORD
nonn,base,easy
AUTHOR
M. F. Hasler, Feb 09 2020
STATUS
approved