A332140 a(n) = 4*(10^(2*n+1) - 1)/9 - 4*10^n.

0, 404, 44044, 4440444, 444404444, 44444044444, 4444440444444, 444444404444444, 44444444044444444, 4444444440444444444, 444444444404444444444, 44444444444044444444444, 4444444444440444444444444, 444444444444404444444444444, 44444444444444044444444444444, 4444444444444440444444444444444

Offset

0,2

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) = A002278(2*n+1) - 4*10^n.

G.f.: 4*x*(101 - 200*x)/((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.

From Elmo R. Oliveira, Dec 12 2025: (Start)

a(n) = 2*A332120(n).

E.g.f.: 4*exp(x)*(10*exp(99*x) - 9*exp(9*x) - 1)/9. (End)

Maple

A332140 := n -> 4*((10^(2*n+1)-1)/9-10^n);

Mathematica

Array[4 ((10^(2 # + 1)-1)/9 - 10^#) &, 15, 0]
LinearRecurrence[{111, -1110, 1000}, {0, 404, 44044}, 20] (* Harvey P. Dale, Jul 06 2021 *)

Prog

(PARI) apply( {A332140(n)=(10^(n*2+1)\9-10^n)*4}, [0..15])
(Python) def A332140(n): return (10**(n*2+1)//9-10**n)*4

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. A332120 .. A332190 (variants with different repeated digit 2, ..., 9).

Cf. A332141 .. A332149 (variants with different middle digit 1, ..., 9).

Cf. A332120.

Sequence in context: A187382 A306308 A185638 * A198536 A337047 A169904

Adjacent sequences: A332137 A332138 A332139 * A332141 A332142 A332143

Keyword

nonn,base,easy

Author

M. F. Hasler, Feb 09 2020

Status

approved