A332128 a(n) = 2*(10^(2n+1)-1)/9 + 6*10^n.

8, 282, 22822, 2228222, 222282222, 22222822222, 2222228222222, 222222282222222, 22222222822222222, 2222222228222222222, 222222222282222222222, 22222222222822222222222, 2222222222228222222222222, 222222222222282222222222222, 22222222222222822222222222222, 2222222222222228222222222222222

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) + 8*10^n = A002276(2n+1) + 6*10^n = 2*A332114(n).

G.f.: (8 - 606*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

A332128 := n -> 2*(10^(2*n+1)-1)/9+6*10^n;

Mathematica

Array[2 (10^(2 # + 1)-1)/9 + 6*10^# &, 15, 0]

Prog

(PARI) apply( {A332128(n)=10^(n*2+1)\9*2+6*10^n}, [0..15])
(Python) def A332128(n): return 10**(n*2+1)//9*2+6*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. A332118 .. A332178, A181965 (variants with different repeated digit 1, ..., 9).

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

Sequence in context: A226415 A226346 A217488 * A247484 A136364 A089670

Adjacent sequences: A332125 A332126 A332127 * A332129 A332130 A332131

Keyword

nonn,base,easy

Author

M. F. Hasler, Feb 09 2020

Status

approved