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%I #39 Feb 13 2023 09:02:29
%S 1,2,8,24,64,160,384,896,2048,4608,10240,22528,49152,106496,229376,
%T 491520,1048576,2228224,4718592,9961472,20971520,44040192,92274688,
%U 192937984,402653184,838860800,1744830464,3623878656,7516192768
%N Row sums of triangle A134400.
%C Essentially the same sequence as A036289.
%C An elephant sequence, see A175654. For the corner squares four A[5] vectors, with decimal values 187, 190, 250 and 442, lead to this sequence. For the central square these vectors lead to the companion sequence 2*A001792, for n >= 1 and a(0)=1. - _Johannes W. Meijer_, Aug 15 2010
%C Number of vertices on a partially truncated n-cube (column 1 of A271316). - _Vincent J. Matsko_, Apr 07 2016
%H Muniru A Asiru, <a href="/A134401/b134401.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4).
%F Binomial transform of repeats of (4n+1): [1, 1, 5, 5, 9, 9, 13, 13, ...].
%F a(n) = n*2^n, n > 1. - Eugeny Yakimovitch (Eugeny.Yakimovitch(AT)gmail.com), Jan 08 2008
%F From _Colin Barker_, Jul 29 2012: (Start)
%F a(n) = 4*a(n-1) - 4*a(n-2) for n > 2.
%F G.f.: (1 - 2*x + 4*x^2)/(1-2*x)^2. (End)
%F E.g.f.: 1-E(0) where E(k)=1 - (k+1)/(1 - 2*x/(2*x - (k+1)^2/E(k+1) )); (continued fraction). - _Sergei N. Gladkovskii_, Dec 07 2012
%F a(n) = A097064(n+1) for n >= 1. - _Georg Fischer_, Oct 28 2018
%F E.g.f.: 1 + 2*exp(2*x)*x. - _Stefano Spezia_, Feb 12 2023
%e a(3) = 24 = sum of row 3 terms of triangle A134400: (3 + 9 + 9 + 3).
%e a(3) = 24 = (1, 3, 3, 1) dot (1, 1, 5, 5) = (1 + 3 + 15 + 5).
%p 1,seq(n*2^n,n=1..30); # _Muniru A Asiru_, Oct 28 2018
%t F = Function[x, x*2^x];F[Range[1, 10]] (* Eugeny Yakimovitch (Eugeny.Yakimovitch(AT)gmail.com), Jan 08 2008 *)
%t {1}~Join~Table[n 2^n, {n, 28}] (* or *) Total /@ Join[{{1}}, Table[n Binomial[n, k], {n, 28}, {k, 0, n}]] (* _Michael De Vlieger_, Apr 07 2016 *)
%o (PARI) x='x+O('x^99); Vec((1-2*x+4*x^2)/(1-2*x)^2) \\ _Altug Alkan_, Apr 07 2016
%o (GAP) a:=Concatenation([1],List([1..30],n->n*2^n)); # _Muniru A Asiru_, Oct 28 2018
%Y Cf. A001792, A036289, A097064, A134400, A175654, A271316.
%K nonn,easy
%O 0,2
%A _Gary W. Adamson_, Oct 23 2007
%E More terms from _Johannes W. Meijer_, Aug 15 2010
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