A332141 a(n) = 4*(10^(2*n+1)-1)/9 - 3*10^n.

1, 414, 44144, 4441444, 444414444, 44444144444, 4444441444444, 444444414444444, 44444444144444444, 4444444441444444444, 444444444414444444444, 44444444444144444444444, 4444444444441444444444444, 444444444444414444444444444, 44444444444444144444444444444, 4444444444444441444444444444444

Offset: 0

Author

M. F. Hasler, Feb 09 2020

Keywords

• nonn
• base
• easy

Links

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

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002278 (4*R_n), A011557 (10^n).

Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).

Cf. A332121 .. A332191 (variants with different repeated digit 2, ..., 9).

Cf. A332140 .. A332149 (variants with different middle digit 0, ..., 9).

Programs

Maple

A332141 := n -> 4*(10^(2*n+1)-1)/9-3*10^n;

Mathematica

Array[4 (10^(2 # + 1)-1)/9 - 3*10^# &, 15, 0]
LinearRecurrence[{111,-1110,1000},{1,414,44144},20] (* or *) Table[ FromDigits[Join[PadRight[{},n,4],{1},PadRight[{},n,4]]],{n,0,20}](* Harvey P. Dale, Aug 17 2020 *)

PARI

apply( {A332141(n)=10^(n*2+1)\9*4-3*10^n}, [0..15])

Python

def A332141(n): return 10**(n*2+1)//9*4-3*10**n

Formula

a(n) = 4*A138148(n) + 1*10^n = A002278(2n+1) - 3*10^n.

G.f.: (1 + 303*x - 700*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.