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Number of palindromes (in base 9) below 9^n.
1

%I #14 Jun 13 2015 00:52:05

%S 8,16,88,160,808,1456,7288,13120,65608,118096,590488,1062880,5314408,

%T 9565936,47829688,86093440,430467208,774840976,3874204888,6973568800,

%U 34867844008,62762119216,313810596088,564859072960,2824295364808,5083731656656,25418658283288

%N Number of palindromes (in base 9) below 9^n.

%H Colin Barker, <a href="/A117868/b117868.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,9,-9).

%F a(n) = 10*9^((n-1)/2)-2 (n odd), 2*9^(n/2)-2 (n even).

%F a(1)=0, a(2)=8, a(3)=16, a(n)=a(n-1)+9*a(n-2)-9*a(n-3). - _Harvey P. Dale_, Jul 17 2012

%F G.f.: 8*x*(x+1) / ((x-1)*(3*x-1)*(3*x+1)). - _Colin Barker_, Apr 26 2015

%F a(n) = 8 * 3^(n-1) + 2 * (-3)^(n-1) - 2. - _Robert Israel_, Apr 26 2015

%p seq( 8 * 3^(n-1) + 2 * (-3)^(n-1) - 2, n=1..100); # _Robert Israel_, Apr 26 2015

%t Table[If[OddQ[n],10*9^((n-1)/2)-2,2*9^(n/2)-2],{n,0,30}] (* or *) LinearRecurrence[ {1,9,-9},{0,8,16},30] (* _Harvey P. Dale_, Jul 17 2012 *)

%o (PARI) Vec(8*x*(x+1)/((x-1)*(3*x-1)*(3*x+1)) + O(x^100)) \\ _Colin Barker_, Apr 26 2015

%Y Cf. A050250.

%K nonn,base,easy

%O 1,1

%A _Martin Renner_, May 02 2006

%E More terms from _Harvey P. Dale_, Jul 17 2012