A134401 Row sums of triangle A134400.

1, 2, 8, 24, 64, 160, 384, 896, 2048, 4608, 10240, 22528, 49152, 106496, 229376, 491520, 1048576, 2228224, 4718592, 9961472, 20971520, 44040192, 92274688, 192937984, 402653184, 838860800, 1744830464, 3623878656, 7516192768

Offset: 0

Author

Gary W. Adamson, Oct 23 2007

Keywords

• nonn
• easy

Comments

Essentially the same sequence as A036289.

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

Number of vertices on a partially truncated n-cube (column 1 of A271316). - Vincent J. Matsko, Apr 07 2016

Examples

			a(3) = 24 = sum of row 3 terms of triangle A134400: (3 + 9 + 9 + 3).
a(3) = 24 = (1, 3, 3, 1) dot (1, 1, 5, 5) = (1 + 3 + 15 + 5).
		

Links

• Muniru A Asiru, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-4).

Crossrefs

Cf. A001792, A036289, A097064, A134400, A175654, A271316.

Programs

GAP

a:=Concatenation([1],List([1..30],n->n*2^n)); # Muniru A Asiru, Oct 28 2018

Maple

1,seq(n*2^n,n=1..30); # Muniru A Asiru, Oct 28 2018

Mathematica

F = Function[x, x*2^x];F[Range[1, 10]] (* Eugeny Yakimovitch (Eugeny.Yakimovitch(AT)gmail.com), Jan 08 2008 *)
{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 *)

PARI

x='x+O('x^99); Vec((1-2*x+4*x^2)/(1-2*x)^2) \\ Altug Alkan, Apr 07 2016

Formula

Binomial transform of repeats of (4n+1): [1, 1, 5, 5, 9, 9, 13, 13, ...].

a(n) = n*2^n, n > 1. - Eugeny Yakimovitch (Eugeny.Yakimovitch(AT)gmail.com), Jan 08 2008

From Colin Barker, Jul 29 2012: (Start)

a(n) = 4*a(n-1) - 4*a(n-2) for n > 2.

G.f.: (1 - 2*x + 4*x^2)/(1-2*x)^2. (End)

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

a(n) = A097064(n+1) for n >= 1. - Georg Fischer, Oct 28 2018

E.g.f.: 1 + 2*exp(2*x)*x. - Stefano Spezia, Feb 12 2023

Extensions

More terms from Johannes W. Meijer, Aug 15 2010