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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A259824 A Catalan-type triangle read by rows, generated by iteration of convolution squares. 0
1, 1, 1, 1, 2, 2, 1, 3, 6, 4, 1, 4, 13, 16, 8, 1, 5, 24, 46, 40, 16, 1, 6, 40, 114, 140, 96, 32, 1, 7, 52, 266, 424, 392, 224, 64, 1, 8, 79, 526, 1208, 1368, 1040, 512, 128, 1, 9, 114, 1079, 3033, 4432, 4064, 2656, 1152, 256 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

The triangle is generated by an iterative procedure in which the (n+1)-st row of the following array is the convolution square of the n-th row prepended with a 1.

1, 1, 1,  1,  1,  1,   1, ...(given)

1, 2, 3,  4,  5,  6,   7, ...

1, 2, 5, 10, 18, 30,  47, ...

1, 2, 5, 14, 34, 76, 161, ...

...

where the rows converge to the Catalan numbers (A000108).

Example: second row of (1, 2, 3, ...) is prepended with a 1: (1, 1, 2, 3, ...), and the convolution square of that sequence is row 3 (1, 2, 5, 10, 18, ...).

Next, take finite differences of terms by columns; such that the finite difference row of the n-th column becomes the n-th row of the triangle. First few rows of the triangle (as an infinite lower triangular matrix with the rest zeros) are:

1;

1, 1;

1, 2, 2;

1, 3, 6, 4;

1, 4, 13, 16, 8;

1, 5, 24, 46, 40, 16;

1, 6, 40, 114, 140, 96, 32;

1, 7, 52, 266, 424, 392, 224, 64;

...

LINKS

Table of n, a(n) for n=1..55.

EXAMPLE

Row 4 of the triangle is (1, 3, 6, 4, 0, 0, 0, ...) since the finite differences of row 4 of the array (1, 4, 10, 14, 14, ...) are (1, 3, 6, 4, 0, 0, 0, ...).

CROSSREFS

Cf. A000108 (row sums).

Sequence in context: A082137 A091187 A318607 * A065173 A098474 A153199

Adjacent sequences:  A259821 A259822 A259823 * A259825 A259826 A259827

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Jul 05 2015

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 10 12:30 EST 2019. Contains 329895 sequences. (Running on oeis4.)