A332154 a(n) = 5*(10^(2*n+1)-1)/9 - 10^n.

4, 545, 55455, 5554555, 555545555, 55555455555, 5555554555555, 555555545555555, 55555555455555555, 5555555554555555555, 555555555545555555555, 55555555555455555555555, 5555555555554555555555555, 555555555555545555555555555, 55555555555555455555555555555, 5555555555555554555555555555555

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), A002279 (5*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. A332150 .. A332159 (variants with different middle digit 0, ..., 9).

Programs

Maple

A332154 := n -> 5*(10^(2*n+1)-1)/9-10^n;

Mathematica

Array[5 (10^(2 # + 1)-1)/9 - 10^# &, 15, 0]
LinearRecurrence[{111,-1110,1000},{4,545,55455},20] (* or *) Table[FromDigits[Join[PadRight[{},n,5],{4},PadRight[{},n,5]]],{n,0,20}] (* Harvey P. Dale, Mar 09 2025 *)

PARI

apply( {A332154(n)=10^(n*2+1)\9*5-10^n}, [0..15])

Python

def A332154(n): return 10**(n*2+1)//9*5-10**n

Formula

a(n) = 5*A138148(n) + 4*10^n = A002279(2n+1) - 10^n.

G.f.: (4 + 101*x - 600*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.