A332142 a(n) = 4*(10^(2*n+1)-1)/9 - 2*10^n.

2, 424, 44244, 4442444, 444424444, 44444244444, 4444442444444, 444444424444444, 44444444244444444, 4444444442444444444, 444444444424444444444, 44444444444244444444444, 4444444444442444444444444, 444444444444424444444444444, 44444444444444244444444444444, 4444444444444442444444444444444

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) = 4*A138148(n) + 2*10^n = A002278(2n+1) - 2*10^n = 2*A332121(n).

G.f.: (2 + 202*x - 600*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

A332142 := n -> 4*(10^(2*n+1)-1)/9-2*10^n;

Mathematica

Array[4 (10^(2 # + 1)-1)/9 - 2*10^# &, 15, 0]

Prog

(PARI) apply( {A332142(n)=10^(n*2+1)\9*4-2*10^n}, [0..15])
(Python) def A332142(n): return 10**(n*2+1)//9*4-2*10**n

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002278 (4*R_n), A011557 (10^n).

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

Cf. A332112 .. A332192 (variants with different repeated digit 1, ..., 9).

Cf. A332140 .. A332149 (variants with different middle digit 0, ..., 9).

Sequence in context: A154541 A119120 A373552 * A109931 A352498 A326364

Adjacent sequences: A332139 A332140 A332141 * A332143 A332144 A332145

Keyword

nonn,base,easy

Author

M. F. Hasler, Feb 09 2020

Status

approved