A332145 a(n) = 4*(10^(2*n+1)-1)/9 + 10^n.

5, 454, 44544, 4445444, 444454444, 44444544444, 4444445444444, 444444454444444, 44444444544444444, 4444444445444444444, 444444444454444444444, 44444444444544444444444, 4444444444445444444444444, 444444444444454444444444444, 44444444444444544444444444444, 4444444444444445444444444444444

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) + 5*10^n = A002278(2n+1) + 10^n.

G.f.: (5 - 101*x - 300*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

A332145 := 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}, {5, 454, 44544}, 20] (* Harvey P. Dale, Jul 03 2026 *)

Prog

(PARI) apply( {A332145(n)=10^(n*2+1)\9*4+10^n}, [0..15])
(Python) def A332145(n): return 10**(n*2+1)//9*4+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. A332115 .. A332195 (variants with different repeated digit 1, ..., 9).

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

Sequence in context: A300971 A300928 A221626 * A144509 A375262 A240700

Adjacent sequences: A332142 A332143 A332144 * A332146 A332147 A332148

Keyword

nonn,base,easy,changed

Author

M. F. Hasler, Feb 09 2020

Status

approved