A332123 a(n) = 2*(10^(2n+1)-1)/9 + 10^n.

3, 232, 22322, 2223222, 222232222, 22222322222, 2222223222222, 222222232222222, 22222222322222222, 2222222223222222222, 222222222232222222222, 22222222222322222222222, 2222222222223222222222222, 222222222222232222222222222, 22222222222222322222222222222, 2222222222222223222222222222222

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) = 2*A138148(n) + 3*10^n = A002276(2n+1) + 10^n.

G.f.: (3 - 101*x - 100*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

A332123 := n -> 2*(10^(2*n+1)-1)/9+10^n;

Mathematica

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

Prog

(PARI) apply( {A332123(n)=10^(n*2+1)\9*2+10^n}, [0..15])
(Python) def A332123(n): return 10**(n*2+1)//9*2+10**n

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002276 (2*R_n), A011557 (10^n).

Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).

Cf. A332113 .. A332193 (variants with different repeated digit 1, ..., 9).

Cf. A332120 .. A332129 (variants with different middle digit 0, ..., 9).

Sequence in context: A228871 A195500 A099426 * A100201 A159807 A065580

Adjacent sequences: A332120 A332121 A332122 * A332124 A332125 A332126

Keyword

nonn,base,easy

Author

M. F. Hasler, Feb 09 2020

Status

approved