A332143 a(n) = 4*(10^(2*n+1)-1)/9 - 10^n.

3, 434, 44344, 4443444, 444434444, 44444344444, 4444443444444, 444444434444444, 44444444344444444, 4444444443444444444, 444444444434444444444, 44444444444344444444444, 4444444444443444444444444, 444444444444434444444444444, 44444444444444344444444444444, 4444444444444443444444444444444

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) + 3*10^n = A002278(2n+1) - 10^n.

G.f.: (3 + 101*x - 500*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

A332143 := n -> 4*(10^(2*n+1)-1)/9-10^n;

Mathematica

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

Prog

(PARI) apply( {A332143(n)=10^(n*2+1)\9*4-10^n}, [0..15])
(Python) def A332143(n): return 10**(n*2+1)//9*4-10**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. A332113 .. A332193 (variants with different repeated digit 1, ..., 9).

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

Sequence in context: A229751 A172859 A087771 * A277234 A269553 A361886

Adjacent sequences: A332140 A332141 A332142 * A332144 A332145 A332146

Keyword

nonn,base,easy

Author

M. F. Hasler, Feb 09 2020

Status

approved