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Palindromes a(n) = (10^n + 1)*(10^(n+1) + 1).
2

%I #36 Jun 25 2021 01:40:27

%S 22,1111,101101,10011001,1000110001,100001100001,10000011000001,

%T 1000000110000001,100000001100000001,10000000011000000001,

%U 1000000000110000000001,100000000001100000000001,10000000000011000000000001,1000000000000110000000000001

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

%H Colin Barker, <a href="/A319667/b319667.txt">Table of n, a(n) for n = 0..450</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).

%F From _Colin Barker_, Sep 25 2018: (Start)

%F G.f.: 11*(2 - 121*x + 200*x^2) / ((1 - x)*(1 - 10*x)*(1 - 100*x)).

%F a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n>2.

%F (End)

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

%p seq((10^n+1)*(10^(n+1)+1),n=0..20); # _Muniru A Asiru_, Sep 26 2018

%o (PARI) a(n) = (10^n+1)*(10^(n+1)+1) \\ _Felix Fröhlich_, Sep 25 2018

%o (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

%o (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

%K nonn,base,easy

%O 0,1

%A _Gabriel Osorio_, Sep 25 2018

%E More terms from _Felix Fröhlich_, Sep 25 2018