A332146 a(n) = 4*(10^(2*n+1)-1)/9 + 2*10^n.

6, 464, 44644, 4446444, 444464444, 44444644444, 4444446444444, 444444464444444, 44444444644444444, 4444444446444444444, 444444444464444444444, 44444444444644444444444, 4444444444446444444444444, 444444444444464444444444444, 44444444444444644444444444444, 4444444444444446444444444444444

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) + 6*10^n = A002278(2n+1) + 2*10^n = 2*A332123(n).

G.f.: (6 - 202*x - 200*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

A332146 := 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( {A332146(n)=10^(n*2+1)\9*4+2*10^n}, [0..15])
(Python) def A332146(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. A332116 .. A332196 (variants with different repeated digit 2, ..., 9).

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

Sequence in context: A267082 A051735 A024084 * A132590 A112945 A220865

Adjacent sequences: A332143 A332144 A332145 * A332147 A332148 A332149

Keyword

nonn,base,easy

Author

_M. F. Hasler_, Feb 09 2020

Status

approved