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%I #24 Jan 25 2020 18:05:34
%S 2,7,26,100,392,1552,6176,24640,98432,393472,1573376,6292480,25167872,
%T 100667392,402661376,1610629120,6442483712,25769869312,103079346176,
%U 412317122560,1649267965952,6597070815232,26388281163776
%N a(n) is the sum of all integers from 2^(n-2)+1 to 2^(n-1).
%C Name when submitted: Sum of even-indexed terms of n-th row of array T given by A049773 (from _Clark Kimberling_).
%C Also sum of integers of which the binary order [A029837] is n: a(n) = Sum_[x | ceiling(log_2(x)) = n ]. E.g., a(7) = 6176 = Apply[Plus, Table[w,{w,65,128}]].
%C This sequence may be obtained by filling a complete binary tree left-to-right, row by row with the integers onwards from 2 and then collecting the sums of the rows; e.g., 2, 3+4, 5+6+7+8, 9+10+11+12+13+14+15+16, etc. a(n) is then equal to the sum of row n-1. - _Carl R. White_, Aug 19 2003
%C If the offset is set to zero, the inverse binomial transform gives A007051 without its leading 1. - _R. J. Mathar_, Mar 26 2009
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-8).
%F a(n) = 2^(n-3)*(3*2^(n-2)+1). - _Carl R. White_, Aug 19 2003
%F From _Philippe Deléham_, Feb 20 2004: (Start)
%F a(n+1) = 4*a(n) - 2^(n-2); see also A007582.
%F a(n+1) = 2^(n-2)*A004119(n). (End)
%F From _R. J. Mathar_, Mar 26 2009: (Start)
%F a(n) = 6*a(n-1) - 8*a(n-2).
%F G.f.: -x^2*(-2+5*x)/((4*x-1)*(2*x-1)). (End)
%e a(2) = 2 = 2.
%e a(3) = 7 = 3 + 4.
%e a(4) =26 = 5 + 6 + 7 + 8.
%e ..
%t LinearRecurrence[{6,-8},{2,7},30] (* _Harvey P. Dale_, Mar 04 2013 *)
%Y Cf. A049773 (sequence motivating the original definition).
%Y Cf. A049775(n+2) = A007582(n+1) - A007582(n).
%Y Cf. A029837, A003070.
%K nonn
%O 2,1
%A _Clark Kimberling_
%E More terms from _Michael Somos_
%E Name change by _Olivier Gérard_, Oct 24 2017
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