A332196 a(n) = 10^(2n+1) - 1 - 3*10^n.

6, 969, 99699, 9996999, 999969999, 99999699999, 9999996999999, 999999969999999, 99999999699999999, 9999999996999999999, 999999999969999999999, 99999999999699999999999, 9999999999996999999999999, 999999999999969999999999999, 99999999999999699999999999999

Offset

0,1

Links

Table of n, a(n) for n=0..14.

Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

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

Adjacent sequences: A332193 A332194 A332195 * A332197 A332198 A332199

Keyword

nonn,base,easy

Author

M. F. Hasler, Feb 08 2020

Status

approved