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URL: https://oeis.org/A332120

⇱ A332120 - OEIS

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A332120
a(n) = 2*(10^(2n+1)-1)/9 - 2*10^n.
16
0, 202, 22022, 2220222, 222202222, 22222022222, 2222220222222, 222222202222222, 22222222022222222, 2222222220222222222, 222222222202222222222, 22222222222022222222222, 2222222222220222222222222, 222222222222202222222222222, 22222222222222022222222222222, 2222222222222220222222222222222
OFFSET
0,2
FORMULA
a(n) = 2*A138148(n) = A002276(2n+1) - 2*10^n.
G.f.: 2*x*(101 - 200*x)/((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.
E.g.f.: 2*exp(x)*(10*exp(99*x) - 9*exp(9*x) - 1)/9. - Stefano Spezia, Jul 13 2024
MAPLE
A332120 := n -> 2*((10^(2*n+1)-1)/9-10^n);
MATHEMATICA
Array[2 ((10^(2 # + 1)-1)/9 - 10^#) &, 15, 0]
PROG
(PARI) apply( {A332120(n)=(10^(n*2+1)\9-10^n)*2}, [0..15])
(Python) def A332120(n): return (10**(n*2+1)//9-10**n)*2
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. A332130 .. A332190 (variants with different repeated digit 3, ..., 9).
Cf. A332121 .. A332129 (variants with different middle digit 1, ..., 9).
Sequence in context: A252987 A229640 A221892 * A064100 A159382 A209501
KEYWORD
nonn,base,easy
AUTHOR
M. F. Hasler, Feb 09 2020
STATUS
approved