A332129 a(n) = 2*(10^(2n+1)-1)/9 + 7*10^n.

9, 292, 22922, 2229222, 222292222, 22222922222, 2222229222222, 222222292222222, 22222222922222222, 2222222229222222222, 222222222292222222222, 22222222222922222222222, 2222222222229222222222222, 222222222222292222222222222, 22222222222222922222222222222, 2222222222222229222222222222222

Offset

0,1

Links

Table of n, a(n) for n=0..15.

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

Formula

a(n) = 2*A138148(n) + 9*10^n = A002276(2n+1) + 7*10^n.

G.f.: (9 - 707*x + 500*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

A332129 := n -> 2*(10^(2*n+1)-1)/9+7*10^n;

Mathematica

Array[2 (10^(2 # + 1)-1)/9 + 7*10^# &, 15, 0]
LinearRecurrence[{111, -1110, 1000}, {9, 292, 22922}, 20] (* Harvey P. Dale, Jun 25 2020 *)

Prog

(PARI) apply( {A332129(n)=10^(n*2+1)\9*2+7*10^n}, [0..15])
(Python) def A332129(n): return 10**(n*2+1)//9*2+7*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. A332119 .. A332189 (variants with different repeated digit 1, ..., 8).

Cf. A332120 .. A332128 (variants with different middle digit 0, ..., 8).

Sequence in context: A322243 A364115 A053935 * A086699 A027834 A175823

Adjacent sequences: A332126 A332127 A332128 * A332130 A332131 A332132

Keyword

nonn,base,easy

Author

M. F. Hasler, Feb 09 2020

Status

approved