login
A319667
Palindromes a(n) = (10^n + 1)*(10^(n+1) + 1).
2
22, 1111, 101101, 10011001, 1000110001, 100001100001, 10000011000001, 1000000110000001, 100000001100000001, 10000000011000000001, 1000000000110000000001, 100000000001100000000001, 10000000000011000000000001, 1000000000000110000000000001
OFFSET
0,1
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)
EXAMPLE
For n = 3: (10^3 + 1)(10^4 + 1) = 1001 * 10001 = 10011001, so a(3) = 10011001.
MAPLE
seq((10^n+1)*(10^(n+1)+1), n=0..20); # Muniru A Asiru, Sep 26 2018
PROG
(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
(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
CROSSREFS
Sequence in context: A223715 A255957 A209728 * A038695 A160259 A055475
KEYWORD
nonn,base,easy
AUTHOR
Gabriel Osorio, Sep 25 2018
EXTENSIONS
More terms from Felix Fröhlich, Sep 25 2018
STATUS
approved