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A332196
a(n) = 10^(2n+1) - 1 - 3*10^n.
7
6, 969, 99699, 9996999, 999969999, 99999699999, 9999996999999, 999999969999999, 99999999699999999, 9999999996999999999, 999999999969999999999, 99999999999699999999999, 9999999999996999999999999, 999999999999969999999999999, 99999999999999699999999999999
OFFSET
0,1
FORMULA
a(n) = 9*A138148(n) + 6*10^n.
G.f.: (6 + 303*x - 1200*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.: exp(x)*(10*exp(99*x) - 3*exp(9*x) - 1). - Stefano Spezia, Jul 13 2024
MAPLE
A332196 := n -> 10^(n*2+1)-1-3*10^n;
MATHEMATICA
Array[ 10^(2 # + 1) - 1 - 3*10^# &, 15, 0]
FromDigits/@Table[Join[PadLeft[{6}, n, 9], PadRight[{}, n-1, 9]], {n, 30}] (* or *) LinearRecurrence[{111, -1110, 1000}, {6, 969, 99699}, 30] (* Harvey P. Dale, May 03 2021 *)
PROG
(PARI) apply( {A332196(n)=10^(n*2+1)-1-3*10^n}, [0..15])
(Python) def A332196(n): return 10**(n*2+1)-1-3*10^n
CROSSREFS
Cf. A002275 (repunits R_n = (10^n-1)/9), A002283 (9*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits only), A002113 (palindromes).
Cf. A332116 .. A332186 (variants with different repeated digit 1, ..., 8).
Cf. A332190 .. A332197, A181965 (variants with different middle digit 0, ..., 8).
Sequence in context: A266598 A250392 A145250 * A375020 A024085 A080474
KEYWORD
nonn,base,easy
AUTHOR
M. F. Hasler, Feb 08 2020
STATUS
approved