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Number of palindromes (in base 6) below 6^n.
1

%I #12 Oct 27 2016 03:16:49

%S 5,10,40,70,250,430,1510,2590,9070,15550,54430,93310,326590,559870,

%T 1959550,3359230,11757310,20155390,70543870,120932350,423263230,

%U 725594110,2539579390,4353564670,15237476350,26121388030,91424858110,156728328190,548549148670

%N Number of palindromes (in base 6) below 6^n.

%H G. C. Greubel, <a href="/A117865/b117865.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 (1,6,-6).

%F a(n) = 7*6^((n-1)/2)-2 (n odd), 2*6^(n/2)-2 (n even).

%F G.f.: 5*x*(x+1) / ((x-1)*(6*x^2-1)). - _Colin Barker_, Feb 15 2013

%t Table[If[OddQ[n], 7*6^((n - 1)/2) - 2, 2*6^(n/2) - 2], {n,25}] (* or *) LinearRecurrence[{1,6,-6},{5, 10, 40},25] (* _G. C. Greubel_, Oct 27 2016 *)

%Y Cf. A050250.

%K nonn,base,easy

%O 1,1

%A _Martin Renner_, May 02 2006

%E More terms from _Colin Barker_, Feb 15 2013