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A225810 a(n) = (10^n)^2 + 4*(10^n) + 1. 1
6, 141, 10401, 1004001, 100040001, 10000400001, 1000004000001, 100000040000001, 10000000400000001, 1000000004000000001, 100000000040000000001, 10000000000400000000001, 1000000000004000000000001, 100000000000040000000000001, 10000000000000400000000000001 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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...n...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).

FORMULA

a(n) = 111*a(n-1)-1110*a(n-2)+1000*a(n-3). - Colin Barker, Apr 27 2015

G.f.: -3*(470*x^2-175*x+2) / ((x-1)*(10*x-1)*(100*x-1)). - Colin Barker, Apr 27 2015

MATHEMATICA

Table[(10^n)^2 + 4*(10^n) + 1, {n, 0, 20}] (* T. D. Noe, Aug 12 2013 *)

LinearRecurrence[{111, -1110, 1000}, {6, 141, 10401}, 20] (* Harvey P. Dale, Oct 28 2017 *)

PROG

(PARI) Vec(-3*(470*x^2-175*x+2)/((x-1)*(10*x-1)*(100*x-1)) + O(x^100)) \\ Colin Barker, Apr 27 2015

CROSSREFS

Sequence in context: A059488 A241015 A245986 * A067196 A286446 A048863

Adjacent sequences:  A225807 A225808 A225809 * A225811 A225812 A225813

KEYWORD

nonn,easy

AUTHOR

Lance J. Weingartz, Jul 29 2013

STATUS

approved

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Last modified September 21 14:54 EDT 2020. Contains 337272 sequences. (Running on oeis4.)