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

0,1

Links

Colin Barker, Table of n, a(n) for n = 0..450

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

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

Adjacent sequences: A319664 A319665 A319666 * A319668 A319669 A319670

Keyword

nonn,base,easy

Author

Gabriel Osorio, Sep 25 2018

Extensions

More terms from Felix Fröhlich, Sep 25 2018

Status

approved