# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a206918
Showing 1-1 of 1

%I A206918 #19 Jul 03 2023 20:10:13
%S A206918 0,1,4,16,40,136,328,1096,2632,8776,21064,70216,168520,561736,1348168,
%T A206918 4493896,10785352,35951176,86282824,287609416,690262600,2300875336,
%U A206918 5522100808,18407002696,44176806472,147256021576,353414451784,1178048172616,2827315614280
%N A206918 Sum of binary palindromes p < 2^n.
%C A206918 Partial sums of A206917.
%C A206918 Partial sums of A052955(n) terms of A006995; for example: A052955(4)=7, the sum of the first 7 terms of A006995 is 0+1+3+5+7+15+17=40 which equals a(4).
%H A206918 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1, 8, -8).
%F A206918 a(n) = sum(k=0..n, A206917(k)).
%F A206918 a(n) = sum(k=1..A052955(n), A006995(k)).
%F A206918 a(n) = sum(k=1..(1/2)*(5-(-1)^n)*2^floor(n/2)-1, A006995(k)).
%F A206918 a(n) = (8/7)*((3/4)*((4-(-1)^n)/(3+(-1)^n))*2^(3*floor(n/2))-1).
%F A206918 G.f.: x*(1+3*x+4*x^2)/((x-1)*(8*x^2-1)). - _Alois P. Heinz_, Feb 28 2012
%e A206918 a(0) = 0, since p=0 is the only binary palindrome p<2^0;
%e A206918 a(3) = 16, since p=0, 1, 3, 5, 7 are the only binary palindromes < 2^3 and 0+1+3+5+7=16.
%Y A206918 Cf. A006995, A206820.
%Y A206918 See A016116 for the number of binary palindromes between 2^(n-1) and 2^n.
%Y A206918 See A052995 for the number of binary palindromes < 2^n.
%Y A206918 See A206917 for the sum of binary palindromes between 2^(n-1) and 2^n.
%K A206918 nonn,base,easy
%O A206918 0,3
%A A206918 _Hieronymus Fischer_, Feb 18 2012

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE