

A134401


Row sums of triangle A134400.


5



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 ncube (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(n1)  4*a(n2) for n > 2.
G.f.: (1  2*x + 4*x^2)/(12*x)^2. (End)
E.g.f.: 1E(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((12*x+4*x^2)/(12*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



