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%I A084634 #35 Mar 21 2023 07:14:23
%S A084634 1,2,4,9,21,48,106,227,475,978,1992,4029,8113,16292,32662,65415,
%T A084634 130935,261990,524116,1048385,2096941,4194072,8388354,16776939,
%U A084634 33554131,67108538,134217376,268435077,536870505,1073741388,2147483182,4294966799,8589934063
%N A084634 Binomial transform of 1, 1, 1, 2, 2, 2, 2, 2, ...
%C A084634 Partial sums of A000325.
%H A084634 Vincenzo Librandi, <a href="/A084634/b084634.txt">Table of n, a(n) for n = 0..1000</a>
%H A084634 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5,-9,7,-2).
%F A084634 a(n) = 2^(n+1) - (n^2 + n + 2)/2.
%F A084634 a(n) = 1 + n + n*(n-1)/2 + 2*Sum_{k=3..n} C(n, k).
%F A084634 O.g.f.: (1-3*x+3*x^2)/((1-2*x)*(1-x)^3). - _R. J. Mathar_, Apr 07 2008
%F A084634 a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4). - _R. J. Mathar_, Apr 07 2008
%F A084634 a(n) = Sum_{i=0..n} (2^i - i). - _Ctibor O. Zizka_, Oct 15 2010
%F A084634 a(n) = A000225(n+1) - binomial(n+1,2). - _G. C. Greubel_, Mar 18 2023
%p A084634 A084634:=n->2^(n+1) - (n^2 +n +2)/2; seq(A084634(n), n=0..50); # _Wesley Ivan Hurt_, Jan 31 2014
%t A084634 LinearRecurrence[{5,-9,7,-2}, {1,2,4,9}, 50] (* _Vladimir Joseph Stephan Orlovsky_, Feb 19 2012 *)
%o A084634 (Sage) [2^(n+1)-1-binomial(n+1,2) for n in range(52)] # _Zerinvary Lajos_, May 29 2009
%o A084634 (Magma) [2^(n+1)-1-Binomial(n+1,2): n in [0..50]]; // _G. C. Greubel_, Mar 18 2023
%Y A084634 Cf. A000225, A000325,
%K A084634 nonn,easy
%O A084634 0,2
%A A084634 _Paul Barry_, Jun 06 2003

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