Logo

Greetings from The On-Line Encyclopedia of Integer Sequences!

Hints

Search: id:A124216
Displaying 1-1 of 1 results found. page 1
     Format: long | short | internal | text      Sort: relevance | references | number      Highlight: on | off
A124216 Generalized Pascal triangle. +0
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; listen)
OFFSET

0,5

COMMENT

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.

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 (qntmpkt(AT)yahoo.com), 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: A060102 A152237 A082043 this_sequence A008459 A157192 A154982

Adjacent sequences: A124213 A124214 A124215 this_sequence A124217 A124218 A124219

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry (pbarry(AT)wit.ie), Oct 19 2006

page 1

Search completed in 0.002 seconds

Lookup | Welcome | Find friends | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
More pages | Superseeker | Maintained by N. J. A. Sloane (njas@research.att.com)

Last modified November 25 20:09 EST 2009. Contains 167514 sequences.


AT&T Labs Research