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A332142
a(n) = 4*(10^(2*n+1)-1)/9 - 2*10^n.
1
2, 424, 44244, 4442444, 444424444, 44444244444, 4444442444444, 444444424444444, 44444444244444444, 4444444442444444444, 444444444424444444444, 44444444444244444444444, 4444444444442444444444444, 444444444444424444444444444, 44444444444444244444444444444, 4444444444444442444444444444444
OFFSET
0,1
FORMULA
a(n) = 4*A138148(n) + 2*10^n = A002278(2n+1) - 2*10^n = 2*A332121(n).
G.f.: (2 + 202*x - 600*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
A332142 := n -> 4*(10^(2*n+1)-1)/9-2*10^n;
MATHEMATICA
Array[4 (10^(2 # + 1)-1)/9 - 2*10^# &, 15, 0]
PROG
(PARI) apply( {A332142(n)=10^(n*2+1)\9*4-2*10^n}, [0..15])
(Python) def A332142(n): return 10**(n*2+1)//9*4-2*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. A332112 .. A332192 (variants with different repeated digit 1, ..., 9).
Cf. A332140 .. A332149 (variants with different middle digit 0, ..., 9).
Sequence in context: A154541 A119120 A373552 * A109931 A352498 A326364
KEYWORD
nonn,base,easy
AUTHOR
M. F. Hasler, Feb 09 2020
STATUS
approved