login
A332141
a(n) = 4*(10^(2*n+1)-1)/9 - 3*10^n.
2
1, 414, 44144, 4441444, 444414444, 44444144444, 4444441444444, 444444414444444, 44444444144444444, 4444444441444444444, 444444444414444444444, 44444444444144444444444, 4444444444441444444444444, 444444444444414444444444444, 44444444444444144444444444444, 4444444444444441444444444444444
OFFSET
0,2
FORMULA
a(n) = 4*A138148(n) + 1*10^n = A002278(2n+1) - 3*10^n.
G.f.: (1 + 303*x - 700*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
A332141 := 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}, {1, 414, 44144}, 20] (* or *) Table[ FromDigits[Join[PadRight[{}, n, 4], {1}, PadRight[{}, n, 4]]], {n, 0, 20}](* Harvey P. Dale, Aug 17 2020 *)
PROG
(PARI) apply( {A332141(n)=10^(n*2+1)\9*4-3*10^n}, [0..15])
(Python) def A332141(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. A332121 .. A332191 (variants with different repeated digit 2, ..., 9).
Cf. A332140 .. A332149 (variants with different middle digit 0, ..., 9).
Sequence in context: A236149 A231312 A210304 * A187864 A190028 A184545
KEYWORD
nonn,base,easy
AUTHOR
M. F. Hasler, Feb 09 2020
STATUS
approved