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

0,1

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) = 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.

Maple

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

Mathematica

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

Prog

(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

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).

Sequence in context: A341871 A226263 A029590 * A291953 A225206 A268207

Adjacent sequences: A332153 A332154 A332155 * A332157 A332158 A332159

Keyword

nonn,base,easy

Author

M. F. Hasler, Feb 09 2020

Status

approved