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A134401 Row sums of triangle A134400. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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. A036289, A097064, A134400.

Sequence in context: A131135 A292218 A097064 * A036289 A294458 A229136

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

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Last modified May 21 02:48 EDT 2019. Contains 323434 sequences. (Running on oeis4.)