login
This site is supported by donations to The OEIS Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A112743 An aerated Delannoy triangle. 0
1, 0, 1, 1, 0, 1, 0, 3, 0, 1, 1, 0, 5, 0, 1, 0, 5, 0, 7, 0, 1, 1, 0, 13, 0, 9, 0, 1, 0, 7, 0, 25, 0, 11, 0, 1, 1, 0, 25, 0, 41, 0, 13, 0, 1, 0, 9, 0, 63, 0, 61, 0, 15, 0, 1, 1, 0, 41, 0, 129, 0, 85, 0, 17, 0, 1, 0, 11, 0, 129, 0, 231, 0, 113, 0, 19, 0, 1, 1, 0, 61, 0, 321, 0, 377, 0, 145, 0, 21, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

Row sums are tribonacci numbers A000073. Diagonal sums are aerated Pell numbers.

LINKS

Table of n, a(n) for n=0..90.

FORMULA

Riordan array (1/(1-x^2), x(1+x^2)/(1-x^2)).

Number triangle T(n,k) = if(k<=n, Sum_{j=0..k} (1+(-1)^(n-k))binomial(k,j)binomial((n-k)/2,j)2^j/2, 0).

T(n,k) = T(n-1,k-1) + T(n-2,k) + T(n-3,k-1). - Philippe Deléham, Mar 11 2013

EXAMPLE

Rows begin

  1;

  0,  1;

  1,  0,  1;

  0,  3,  0,  1;

  1,  0,  5,  0,  1;

  0,  5,  0,  7,  0,  1;

  1,  0, 13,  0,  9,  0,  1;

  0,  7,  0, 25,  0, 11,  0,  1;

  1,  0, 25,  0, 41,  0, 13,  0,  1;

CROSSREFS

Cf. A008288, A114123, A216182.

Sequence in context: A317595 A263753 A303877 * A230427 A229995 A119467

Adjacent sequences:  A112740 A112741 A112742 * A112744 A112745 A112746

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Sep 17 2005

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 January 18 04:47 EST 2019. Contains 319269 sequences. (Running on oeis4.)