A332125 a(n) = 2*(10^(2n+1)-1)/9 + 3*10^n.

5, 252, 22522, 2225222, 222252222, 22222522222, 2222225222222, 222222252222222, 22222222522222222, 2222222225222222222, 222222222252222222222, 22222222222522222222222, 2222222222225222222222222, 222222222222252222222222222, 22222222222222522222222222222, 2222222222222225222222222222222

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) + 5*10^n = A002276(2n+1) + 3*10^n.

G.f.: (5 - 303*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

A332125 := n -> 2*(10^(2*n+1)-1)/9+3*10^n;

Mathematica

Array[2 (10^(2 # + 1)-1)/9 + 3*10^# &, 15, 0]

Prog

(PARI) apply( {A332125(n)=10^(n*2+1)\9*2+3*10^n}, [0..15])
(Python) def A332125(n): return 10**(n*2+1)//9*2+3*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. A332115 .. A332195 (variants with different repeated digit 1, ..., 9).

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

Sequence in context: A308295 A060943 A336295 * A308652 A002770 A069071

Adjacent sequences: A332122 A332123 A332124 * A332126 A332127 A332128

Keyword

nonn,base,easy

Author

M. F. Hasler, Feb 09 2020

Status

approved