A225813 a(n) = (10^n)^2 + 7*(10^n) + 1.

9, 171, 10701, 1007001, 100070001, 10000700001, 1000007000001, 100000070000001, 10000000700000001, 1000000007000000001, 100000000070000000001, 10000000000700000000001, 1000000000007000000000001, 100000000000070000000000001, 10000000000000700000000000001

Offset: 0

Author

Lance J. Weingartz, Jul 29 2013

Keywords

• nonn
• easy

Comments

This is an instance of (10^n)^2 + x(10^n) + 1 which umbrellas A066138, A033934, A171375, A171410, A171461, A171513 and A171553 which all produce palindromes of the form 1...x...1 when n <> 0.

Links

• Colin Barker, Table of n, a(n) for n = 0..499
• Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

Crossrefs

Cf. A033934, A066138, A171375, A171410, A171461, A171513, A171553.

Programs

Maple

A225813:=n->(10^n)^2 + 7*(10^n) + 1: seq(A225813(n), n=0..20); # Wesley Ivan Hurt, Apr 08 2017

Mathematica

Table[(10^n)^2 + 7*(10^n) + 1, {n, 0, 20}] (* T. D. Noe, Aug 12 2013 *)
LinearRecurrence[{111,-1110,1000},{9,171,10701},20] (* Harvey P. Dale, Apr 12 2020 *)

PARI

Vec(-9*(190*x^2-92*x+1)/((x-1)*(10*x-1)*(100*x-1)) + O(x^100)) \\ Colin Barker, Apr 27 2015

Formula

From Colin Barker, Apr 27 2015: (Start)

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

G.f.: -9*(190*x^2-92*x+1)/((x-1)*(10*x-1)*(100*x-1)). (End)

E.g.f.: exp(x)*(1 + 7*exp(9*x) + exp(99*x)). - Elmo R. Oliveira, Jul 04 2025