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A332126
a(n) = 2*(10^(2n+1)-1)/9 + 4*10^n.
3
6, 262, 22622, 2226222, 222262222, 22222622222, 2222226222222, 222222262222222, 22222222622222222, 2222222226222222222, 222222222262222222222, 22222222222622222222222, 2222222222226222222222222, 222222222222262222222222222, 22222222222222622222222222222, 2222222222222226222222222222222
OFFSET
0,1
FORMULA
a(n) = 2*A138148(n) + 6*10^n = A002276(2n+1) + 4*10^n = 2*A332113(n).
G.f.: (6 - 404*x + 200*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.
E.g.f.: 2*exp(x)*(10*exp(99*x) + 18*exp(9*x) - 1)/9. - Stefano Spezia, Jul 13 2024
MAPLE
A332126 := n -> 2*(10^(2*n+1)-1)/9+4*10^n;
MATHEMATICA
Array[2 (10^(2 # + 1)-1)/9 + 4*10^# &, 15, 0]
Table[FromDigits[Join[PadRight[{}, n, 2], {6}, PadRight[{}, n, 2]]], {n, 0, 20}] (* or *) LinearRecurrence[{111, -1110, 1000}, {6, 262, 22622}, 20] (* Harvey P. Dale, Oct 17 2021 *)
PROG
(PARI) apply( {A332126(n)=10^(n*2+1)\9*2+4*10^n}, [0..15])
(Python) def A332126(n): return 10**(n*2+1)//9*2+4*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. A332116 .. A332196 (variants with different repeated digit 1, ..., 9).
Cf. A332120 .. A332129 (variants with different middle digit 0, ..., 9).
Sequence in context: A003384 A316393 A366226 * A229579 A033289 A244493
KEYWORD
nonn,base,easy
AUTHOR
M. F. Hasler, Feb 09 2020
STATUS
approved