A332151 a(n) = 5*(10^(2*n+1)-1)/9 - 4*10^n.

1, 515, 55155, 5551555, 555515555, 55555155555, 5555551555555, 555555515555555, 55555555155555555, 5555555551555555555, 555555555515555555555, 55555555555155555555555, 5555555555551555555555555, 555555555555515555555555555, 55555555555555155555555555555, 5555555555555551555555555555555

Offset: 0

Author

M. F. Hasler, Feb 09 2020

Keywords

• nonn
• base
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..499
• 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. A332121 .. A332191 (variants with different repeated digit 2, ..., 9).

Cf. A332150 .. A332159 (variants with different middle digit 0, ..., 9).

Programs

Maple

A332151 := n -> 5*(10^(2*n+1)-1)/9-4*10^n;

Mathematica

Array[5 (10^(2 # + 1)-1)/9 - 4*10^# &, 15, 0]
Table[With[{c=PadRight[{},n,5]},FromDigits[Join[c,{1},c]]],{n,0,20}] (* Harvey P. Dale, Mar 16 2021 *)

PARI

apply( {A332151(n)=10^(n*2+1)\9*5-4*10^n}, [0..15])

Python

def A332151(n): return 10**(n*2+1)//9*5-4*10**n

Formula

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

G.f.: (1 + 404*x - 900*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.