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A145654 Partial sums of A000918, starting from index 1.

%I A145654 #38 Jul 17 2018 12:29:31
%S A145654 0,2,8,22,52,114,240,494,1004,2026,4072,8166,16356,32738,65504,131038,
%T A145654 262108,524250,1048536,2097110,4194260,8388562,16777168,33554382,
%U A145654 67108812,134217674,268435400,536870854,1073741764,2147483586
%N A145654 Partial sums of A000918, starting from index 1.
%H A145654 Reinhard Zumkeller, <a href="/A145654/b145654.txt">Table of n, a(n) for n = 1..1000</a>
%H A145654 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,2).
%F A145654 a(n) = Sum_{i=1..n} A000918(i).
%F A145654 a(n+1) - a(n) = A000918(n+1).
%F A145654 a(n) = A005803(n+1). - _R. J. Mathar_, Oct 21 2008
%F A145654 From _Colin Barker_, Jan 11 2012: (Start)
%F A145654 a(n) = 2*(-1 + 2^n - n).
%F A145654 G.f.: 2*x^2/((1-x)^2*(1-2*x)). (End)
%F A145654 a(n+1) = A121173(2*n). - _Reinhard Zumkeller_, Nov 06 2013
%F A145654 a(n) = Sum_{i=1..n-1} (n-i)*2^i with a(1)=0. - _Bruno Berselli_, Feb 10 2014
%F A145654 a(n) = 2 * A000295(n). - _Alois P. Heinz_, May 28 2018
%e A145654 For n=7, a(7) = 6*2 + 5*2^2 + 4*2^3 + 3*2^4 + 2*2^5 + 1*2^6 = 240. - _Bruno Berselli_, Feb 10 2014
%e A145654 From _Bruno Berselli_, Jul 17 2018: (Start)
%e A145654 Row sums of the triangle:
%e A145654    0   ......................................    0
%e A145654    1,  1   ..................................    2
%e A145654    3,  2,  3   ..............................    8
%e A145654    6,  5,  5,  6   ..........................   22
%e A145654   10, 11, 10, 11, 10   ......................   52
%e A145654   15, 21, 21, 21, 21, 15   ..................  114
%e A145654   21, 36, 42, 42, 42, 36, 21   ..............  240
%e A145654   28, 57, 78, 84, 84, 78, 57, 28   ..........  494, etc.
%e A145654 (End)
%t A145654 Accumulate[2^Range[30] - 2] (* or *) LinearRecurrence[{4, -5, 2}, {0, 2, 8}, 30] (* _Harvey P. Dale_, Jul 15 2017 *)
%o A145654 (Haskell)
%o A145654 a145654 n = a145654_list !! (n-1)
%o A145654 a145654_list = scanl1 (+) $ tail a000918_list
%o A145654 -- _Reinhard Zumkeller_, Nov 06 2013
%Y A145654 Cf. A000217, A000295, A000918, A005803, A121173.
%K A145654 nonn,easy
%O A145654 1,2
%A A145654 _Vladimir Joseph Stephan Orlovsky_, Oct 16 2008
%E A145654 Edited by _R. J. Mathar_, Oct 21 2008