login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A124216 Generalized Pascal triangle. 2
1, 1, 1, 1, 4, 1, 1, 9, 9, 1, 1, 16, 34, 16, 1, 1, 25, 90, 90, 25, 1, 1, 36, 195, 328, 195, 36, 1, 1, 49, 371, 931, 931, 371, 49, 1, 1, 64, 644, 2240, 3334, 2240, 644, 64, 1, 1, 81, 1044, 4788, 9846, 9846 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Consider the 1-parameter family of triangles with g.f. (1-x(1+y))/(1-2x(1+y)+x^2(1+k*x+y^2)). A007318 corresponds to k=2. A056241 corresponds to k=1. A124216 corresponds to k=0. Row sums are A006012. Diagonal sums are A124217.

LINKS

Table of n, a(n) for n=0..50.

P. Barry, On a Generalization of the Narayana Triangle, J. Int. Seq. 14 (2011) # 11.4.5

FORMULA

G.f.: (1-x(1+y))/(1-2x(1+y)+x^2(1+y^2)); Number triangle T(n,k)=sum{j=0..n, C(n,j)C(j,2(j-k))2^(j-k)}.

Equals 2*A001263 - A007318; (i.e. twice the Narayana triangle minus Pascal's triangle). - Gary W. Adamson, Jun 14 2007

EXAMPLE

Triangle begins

1,

1, 1,

1, 4, 1,

1, 9, 9, 1,

1, 16, 34, 16, 1,

1, 25, 90, 90, 25, 1,

1, 36, 195, 328, 195, 36, 1,

1, 49, 371, 931, 931, 371, 49, 1

CROSSREFS

Cf. A001263.

Sequence in context: A082043 A177944 A174006 * A008459 A259333 A180960

Adjacent sequences: A124213 A124214 A124215 * A124217 A124218 A124219

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Oct 19 2006

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 5 15:27 EST 2022. Contains 358588 sequences. (Running on oeis4.)