A033934 a(n) = (10^n + 1)^2.

4, 121, 10201, 1002001, 100020001, 10000200001, 1000002000001, 100000020000001, 10000000200000001, 1000000002000000001, 100000000020000000001, 10000000000200000000001, 1000000000002000000000001, 100000000000020000000000001, 10000000000000200000000000001

Offset: 0

Author

Jeff Burch

Keywords

• nonn
• base
• easy

Comments

The members of this sequence are both perfect squares and palindromes. Therefore A002779 is an infinite sequence. - Ant King, Jun 26 2011

Links

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

Crossrefs

Cf. A002779 (palindromic squares), A000290 (squares), A002113 (palindromes).

Cf. A011557, A062397, A066138.

Programs

Mathematica

(10^Range[0,20]+1)^2 (* or *) LinearRecurrence[{111,-1110,1000},{4,121,10201},20] (* Harvey P. Dale, Feb 16 2016 *)

PARI

my(x='x+O('x^15)); Vec((1210*x^2-323*x+4)/(-1000*x^3+1110*x^2-111*x+1)) \\ Elmo R. Oliveira, Jul 04 2025

Formula

a(n) = A062397(n)^2 = A066138(n) + A011557(n).

From Elmo R. Oliveira, Jul 04 2025: (Start)

G.f.: (4 - 323*x + 1210*x^2)/((1-x)*(1-10*x)*(1-100*x)).

E.g.f.: exp(x)*(1 + 2*exp(9*x) + exp(99*x)).

a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3). (End)

Extensions

Better description from Henry Bottomley, Dec 07 2001

More terms from Harvey P. Dale, Feb 16 2016