A319667 Palindromes a(n) = (10^n + 1)*(10^(n+1) + 1).

22, 1111, 101101, 10011001, 1000110001, 100001100001, 10000011000001, 1000000110000001, 100000001100000001, 10000000011000000001, 1000000000110000000001, 100000000001100000000001, 10000000000011000000000001, 1000000000000110000000000001

Offset: 0

Author

Gabriel Osorio, Sep 25 2018

Keywords

• nonn
• base
• easy

Examples

			For n = 3: (10^3 + 1)(10^4 + 1) = 1001 * 10001 = 10011001, so a(3) = 10011001.
		

Links

• Colin Barker, Table of n, a(n) for n = 0..450
• Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

Programs

GAP

a:=[22,1111,101101];; for n in [4..20] do a[n]:=111*a[n-1]-1110*a[n-2]+1000*a[n-3]; od; a; # Muniru A Asiru, Sep 26 2018

Maple

seq((10^n+1)*(10^(n+1)+1),n=0..20); # Muniru A Asiru, Sep 26 2018

PARI

a(n) = (10^n+1)*(10^(n+1)+1) \\ Felix Fröhlich, Sep 25 2018

PARI

Vec(11*(2 - 121*x + 200*x^2) / ((1 - x)*(1 - 10*x)*(1 - 100*x)) + O(x^15)) \\ Colin Barker, Sep 25 2018

Formula

From Colin Barker, Sep 25 2018: (Start)

G.f.: 11*(2 - 121*x + 200*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.

(End)

Extensions

More terms from Felix Fröhlich, Sep 25 2018