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

0,2

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

Links

Muniru A Asiru, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-4).

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

Example

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).

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 *)

Prog

(PARI) x='x+O('x^99); Vec((1-2*x+4*x^2)/(1-2*x)^2) \\ Altug Alkan, Apr 07 2016
(GAP) a:=Concatenation([1], List([1..30], n->n*2^n)); # Muniru A Asiru, Oct 28 2018

Crossrefs

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

Sequence in context: A006730 A131135 A292218 * A036289 A097064 A352206

Adjacent sequences: A134398 A134399 A134400 * A134402 A134403 A134404

Keyword

nonn,easy

Author

Gary W. Adamson, Oct 23 2007

Extensions

More terms from Johannes W. Meijer, Aug 15 2010

Status

approved