The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A332141 a(n) = 4*(10^(2*n+1)-1)/9 - 3*10^n. 2
1, 414, 44144, 4441444, 444414444, 44444144444, 4444441444444, 444444414444444, 44444444144444444, 4444444441444444444, 444444444414444444444, 44444444444144444444444, 4444444444441444444444444, 444444444444414444444444444, 44444444444444144444444444444, 4444444444444441444444444444444 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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
KEYWORD
nonn,base,easy
AUTHOR
M. F. Hasler, Feb 09 2020
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 20 11:05 EDT 2024. Contains 372712 sequences. (Running on oeis4.)