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A070199 Number of palindromes of length <= n. 3
10, 19, 109, 199, 1099, 1999, 10999, 19999, 109999, 199999, 1099999, 1999999, 10999999, 19999999, 109999999, 199999999, 1099999999, 1999999999, 10999999999, 19999999999, 109999999999, 199999999999, 1099999999999, 1999999999999 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..24.

Index entries for linear recurrences with constant coefficients, signature (1,10,-10).

FORMULA

a(n) = a(n-1)+10*a(n-2)-10*a(n-3). G.f.: x*(10+9*x-10*x^2)/((1-x)*(1-10*x^2)). [Colin Barker, Jun 30 2012]

a(n)=(-2*Sqrt[10]+10^(n/2)*(11+2*Sqrt[10]+(-1)^n*(-11+2*Sqrt[10])))/ (2*Sqrt[10]). - Harvey P. Dale, Mar 18 2016

MATHEMATICA

LinearRecurrence[{1, 10, -10}, {10, 19, 109}, 30] (* Harvey P. Dale, Mar 18 2016 *)

CROSSREFS

Partial sums of A070252.

Sequence in context: A166706 A131495 A060630 * A015445 A220005 A253213

Adjacent sequences:  A070196 A070197 A070198 * A070200 A070201 A070202

KEYWORD

nonn,base,easy

AUTHOR

N. J. A. Sloane and Robert G. Wilson v, May 14 2002

STATUS

approved

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Last modified September 30 23:11 EDT 2016. Contains 276653 sequences.