login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A134058 Triangle read by rows, T(n,k) = 2*binomial(n,k) if k > 0, (0 <= k <= n), left column = (1,2,2,2,...). 7
1, 2, 2, 2, 4, 2, 2, 6, 6, 2, 2, 8, 12, 8, 2, 2, 10, 20, 20, 10, 2, 2, 12, 30, 40, 30, 12, 2, 2, 14, 42, 70, 70, 42, 14, 2, 2, 16, 56, 112, 140, 112, 56, 16, 2, 2, 18, 72, 168, 252, 252, 168, 72, 18, 2 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums = (1, 4, 8, 16, 32, 64, ...). A134059 = analogous triangle, replacing (1,2,2,2,...) with (1,3,3,3,...).

Triangle T(n,k), 0 <= k <= n, read by rows given by [2, -1, 0, 0, 0, 0, 0, ...] DELTA [2, -1, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938. - Philippe Deléham, Oct 07 2007

Equals A028326 for all but the first term. - R. J. Mathar, Jun 08 2008

Warning: the row sums do not give A046055. - N. J. A. Sloane, Jul 08 2009

LINKS

Table of n, a(n) for n=0..54.

FORMULA

Double Pascal's triangle and replace leftmost column with (1,2,2,2,...).

M*A007318, where M = an infinite lower triangular matrix with (1,2,2,2,...) in the main diagonal and the rest zeros.

Sum_{k=0..n} T(n,k)= A151821(n+1). - Philippe Deléham, Sep 17 2009

G.f.: (1+x+y)/(1-x-y). - Vladimir Kruchinin, Apr 09 2015

EXAMPLE

First few rows of the triangle:

  1

  2,  2;

  2,  4,  2;

  2,  6,  6,  2;

  2,  8, 12,  8,  2;

  2, 10, 20, 20, 10,  2;

  ...

MATHEMATICA

T[n_, k_] := SeriesCoefficient[(1+x+y)/(1-x-y), {x, 0, n-k}, {y, 0, k}]; Table[T[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* Jean-François Alcover, Apr 09 2015, after Vladimir Kruchinin *)

CROSSREFS

Cf. A134059.

Sequence in context: A292929 A049627 A278223 * A216955 A086973 A240131

Adjacent sequences:  A134055 A134056 A134057 * A134059 A134060 A134061

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Oct 05 2007

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 1 21:02 EST 2020. Contains 338858 sequences. (Running on oeis4.)