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

0,1

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) + 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.

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 *)

Prog

(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

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).

Sequence in context: A254966 A345455 A261806 * A278143 A119621 A142734

Adjacent sequences: A332144 A332145 A332146 * A332148 A332149 A332150

Keyword

nonn,base,easy

Author

M. F. Hasler, Feb 09 2020

Status

approved