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

0,2

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) = 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.

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 *)

Prog

(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

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).

Sequence in context: A236149 A231312 A210304 * A187864 A190028 A184545

Adjacent sequences: A332138 A332139 A332140 * A332142 A332143 A332144

Keyword

nonn,base,easy

Author

M. F. Hasler, Feb 09 2020

Status

approved