A332148 a(n) = 4*(10^(2*n+1) - 1)/9 + 4*10^n.

8, 484, 44844, 4448444, 444484444, 44444844444, 4444448444444, 444444484444444, 44444444844444444, 4444444448444444444, 444444444484444444444, 44444444444844444444444, 4444444444448444444444444, 444444444444484444444444444, 44444444444444844444444444444, 4444444444444448444444444444444

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) + 8*10^n = A002278(2*n+1) + 4*10^n = 4*A332112(n).

G.f.: (8 - 404*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*A332124(n).

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

Maple

A332148 := n -> 4*((10^(2*n+1)-1)/9+10^n);

Mathematica

Array[4 ((10^(2 # + 1)-1)/9 + 10^#) &, 15, 0]

Prog

(PARI) apply( {A332148(n)=(10^(n*2+1)\9+10^n)*4}, [0..15])
(Python) def A332148(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. A332118 .. A332178, A181965 (variants with different repeated digit 1, ..., 9).

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

Cf. A332124.

Sequence in context: A204564 A152495 A197096 * A109060 A259926 A391956

Adjacent sequences: A332145 A332146 A332147 * A332149 A332150 A332151

Keyword

nonn,base,easy

Author

M. F. Hasler, Feb 09 2020

Status

approved