A332124 a(n) = 2*(10^(2n+1)-1)/9 + 2*10^n.

4, 242, 22422, 2224222, 222242222, 22222422222, 2222224222222, 222222242222222, 22222222422222222, 2222222224222222222, 222222222242222222222, 22222222222422222222222, 2222222222224222222222222, 222222222222242222222222222, 22222222222222422222222222222, 2222222222222224222222222222222

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) + 4*10^n = A002276(2n+1) + 2*10^n = 2*A332112(n).

G.f.: (4 - 202*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.

Maple

A332124 := n -> 2*((10^(2*n+1)-1)/9+10^n);

Mathematica

Array[2 ((10^(2 # + 1)-1)/9 + 10^#) &, 15, 0]
Table[FromDigits[Join[PadRight[{}, n, 2], {4}, PadRight[{}, n, 2]]], {n, 0, 20}] (* or *) LinearRecurrence[{111, -1110, 1000}, {4, 242, 22422}, 20](* Harvey P. Dale, Mar 06 2023 *)

Prog

(PARI) apply( {A332124(n)=(10^(n*2+1)\9+10^n)*2}, [0..15])
(Python) def A332124(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. A332114 .. A332194 (variants with different repeated digit 1, ..., 9).

Cf. A332120 .. A332129 (variants with different middle digit 0, ..., 9).

Sequence in context: A137342 A152793 A042769 * A091792 A300595 A320418

Adjacent sequences: A332121 A332122 A332123 * A332125 A332126 A332127

Keyword

nonn,base,easy

Author

M. F. Hasler, Feb 09 2020

Status

approved