A332156 a(n) = 5*(10^(2*n+1)-1)/9 + 10^n.

6, 565, 55655, 5556555, 555565555, 55555655555, 5555556555555, 555555565555555, 55555555655555555, 5555555556555555555, 555555555565555555555, 55555555555655555555555, 5555555555556555555555555, 555555555555565555555555555, 55555555555555655555555555555, 5555555555555556555555555555555

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. A332116 .. A332196 (variants with different repeated digit 1, ..., 9).

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

Programs

Maple

A332156 := n -> 5*(10^(2*n+1)-1)/9+10^n;

Mathematica

Array[5 (10^(2 # + 1)-1)/9 + 10^# &, 15, 0]

PARI

apply( {A332156(n)=10^(n*2+1)\9*5+10^n}, [0..15])

Python

def A332156(n): return 10**(n*2+1)//9*5+10**n

Formula

a(n) = 5*A138148(n) + 6*10^n = A002279(2n+1) + 10^n.

G.f.: (6 - 101*x - 400*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.

E.g.f.: exp(x)*(50*exp(99*x) + 9*exp(9*x) - 5)/9. - Stefano Spezia, Jul 13 2024