A332154 a(n) = 5*(10^(2*n+1)-1)/9 - 10^n.

4, 545, 55455, 5554555, 555545555, 55555455555, 5555554555555, 555555545555555, 55555555455555555, 5555555554555555555, 555555555545555555555, 55555555555455555555555, 5555555555554555555555555, 555555555555545555555555555, 55555555555555455555555555555, 5555555555555554555555555555555

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) = 5*A138148(n) + 4*10^n = A002279(2n+1) - 10^n.

G.f.: (4 + 101*x - 600*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

A332154 := n -> 5*(10^(2*n+1)-1)/9-10^n;

Mathematica

Array[5 (10^(2 # + 1)-1)/9 - 10^# &, 15, 0]

Prog

(PARI) apply( {A332154(n)=10^(n*2+1)\9*5-10^n}, [0..15])
(Python) def A332154(n): return 10**(n*2+1)//9*5-10**n

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002279 (5*R_n), A011557 (10^n).

Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).

Cf. A332114 .. A332194 (variants with different repeated digit 1, ..., 9).

Cf. A332150 .. A332159 (variants with different middle digit 0, ..., 9).

Sequence in context: A209608 A159367 A012770 * A202032 A267066 A159530

Adjacent sequences: A332151 A332152 A332153 * A332155 A332156 A332157

Keyword

nonn,base,easy

Author

M. F. Hasler, Feb 09 2020

Status

approved