A332120 a(n) = 2*(10^(2n+1)-1)/9 - 2*10^n.

0, 202, 22022, 2220222, 222202222, 22222022222, 2222220222222, 222222202222222, 22222222022222222, 2222222220222222222, 222222222202222222222, 22222222222022222222222, 2222222222220222222222222, 222222222222202222222222222, 22222222222222022222222222222, 2222222222222220222222222222222

Offset

0,2

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

G.f.: 2*x*(101 - 200*x)/((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.: 2*exp(x)*(10*exp(99*x) - 9*exp(9*x) - 1)/9. - Stefano Spezia, Jul 13 2024

Maple

A332120 := n -> 2*((10^(2*n+1)-1)/9-10^n);

Mathematica

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

Prog

(PARI) apply( {A332120(n)=(10^(n*2+1)\9-10^n)*2}, [0..15])
(Python) def A332120(n): return (10**(n*2+1)//9-10**n)*2

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. A332130 .. A332190 (variants with different repeated digit 3, ..., 9).

Cf. A332121 .. A332129 (variants with different middle digit 1, ..., 9).

Sequence in context: A252987 A229640 A221892 * A064100 A159382 A209501

Adjacent sequences: A332117 A332118 A332119 * A332121 A332122 A332123

Keyword

nonn,base,easy

Author

M. F. Hasler, Feb 09 2020

Status

approved