A332150 a(n) = 5*(10^(2n+1)-1)/9 - 5*10^n.

0, 505, 55055, 5550555, 555505555, 55555055555, 5555550555555, 555555505555555, 55555555055555555, 5555555550555555555, 555555555505555555555, 55555555555055555555555, 5555555555550555555555555, 555555555555505555555555555, 55555555555555055555555555555, 5555555555555550555555555555555

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

G.f.: 5*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.

Maple

A332150 := n -> 5*((10^(2*n+1)-1)/9-10^n);

Mathematica

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

Prog

(PARI) apply( {A332150(n)=(10^(n*2+1)\9-10^n)*5}, [0..15])
(Python) def A332150(n): return (10**(n*2+1)//9-10**n)*5

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

Cf. A332151 .. A332159 (variants with different middle digit 1, ..., 9).

Sequence in context: A003791 A003925 A126846 * A336561 A158633 A204954

Adjacent sequences: A332147 A332148 A332149 * A332151 A332152 A332153

Keyword

nonn,base,easy

Author

M. F. Hasler, Feb 09 2020

Status

approved