A332147 a(n) = 4*(10^(2*n+1)-1)/9 + 3*10^n.

7, 474, 44744, 4447444, 444474444, 44444744444, 4444447444444, 444444474444444, 44444444744444444, 4444444447444444444, 444444444474444444444, 44444444444744444444444, 4444444444447444444444444, 444444444444474444444444444, 44444444444444744444444444444, 4444444444444447444444444444444

Offset: 0

Author

M. F. Hasler, Feb 09 2020

Keywords

• nonn
• base
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

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. A332117 .. A332197 (variants with different repeated digit 1, ..., 9).

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

Programs

Maple

A332147 := n -> 4*(10^(2*n+1)-1)/9+3*10^n;

Mathematica

Array[4 (10^(2 # + 1)-1)/9 + 3*10^# &, 15, 0]
LinearRecurrence[{111,-1110,1000},{7,474,44744},20] (* Harvey P. Dale, Mar 08 2022 *)

PARI

apply( {A332147(n)=10^(n*2+1)\9*4+3*10^n}, [0..15])

Python

def A332147(n): return 10**(n*2+1)//9*4+3*10**n

Formula

a(n) = 4*A138148(n) + 7*10^n = A002278(2n+1) + 3*10^n.

G.f.: (7 - 303*x - 100*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.