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%I #24 Jul 03 2023 20:08:55
%S 0,1,3,12,24,96,192,768,1536,6144,12288,49152,98304,393216,786432,
%T 3145728,6291456,25165824,50331648,201326592,402653184,1610612736,
%U 3221225472,12884901888,25769803776,103079215104,206158430208,824633720832,1649267441664,6597069766656
%N Sum of binary palindromes in the half-open interval [2^(n-1), 2^n).
%C First differences of A206918.
%H <a href="/index/Pac#palindromes">Index to sequences related to palindromes</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0, 8).
%F a(n) = (3/8)*2^(n+floor((n+1)/2)).
%F a(n) = 8*a(n-2) for n>3. G.f.: -x*(4*x^2+3*x+1) / (8*x^2-1). - _Colin Barker_, May 31 2013
%e a(0) = 0, since there is no binary palindrome 2^(-1) <= p < 2^0;
%e a(3) = 12, since 2^2 <= p < 2^3 for p = 5 and p = 7.
%K nonn,base,easy
%O 0,3
%A _Hieronymus Fischer_, Feb 18 2012
%E More terms from _Colin Barker_, May 31 2013
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