A332151 a(n) = 5*(10^(2*n+1)-1)/9 - 4*10^n.

1, 515, 55155, 5551555, 555515555, 55555155555, 5555551555555, 555555515555555, 55555555155555555, 5555555551555555555, 555555555515555555555, 55555555555155555555555, 5555555555551555555555555, 555555555555515555555555555, 55555555555555155555555555555, 5555555555555551555555555555555

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..499

Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

Formula

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

G.f.: (1 + 404*x - 900*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

A332151 := n -> 5*(10^(2*n+1)-1)/9-4*10^n;

Mathematica

Array[5 (10^(2 # + 1)-1)/9 - 4*10^# &, 15, 0]
Table[With[{c=PadRight[{}, n, 5]}, FromDigits[Join[c, {1}, c]]], {n, 0, 20}] (* Harvey P. Dale, Mar 16 2021 *)

Prog

(PARI) apply( {A332151(n)=10^(n*2+1)\9*5-4*10^n}, [0..15])
(Python) def A332151(n): return 10**(n*2+1)//9*5-4*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. A332121 .. A332191 (variants with different repeated digit 2, ..., 9).

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

Sequence in context: A257087 A254643 A322883 * A234826 A232574 A282753

Adjacent sequences: A332148 A332149 A332150 * A332152 A332153 A332154

Keyword

nonn,base,easy

Author

M. F. Hasler, Feb 09 2020

Status

approved