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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A162453 Plane partition triangle, row sums = A000219; derived from the Euler transform of [1, 2, 3,...]. 1
1, 1, 2, 1, 2, 3, 1, 5, 3, 4, 1, 5, 9, 4, 5, 1, 9, 15, 12, 5, 6, 1, 9, 24, 24, 15, 6, 7, 1, 14, 36, 46, 30, 18, 7, 8, 1, 14, 58, 70, 65, 36, 21, 8, 9, 1, 20, 76, 130, 110, 78, 42, 24, 9, 10, 1, 20, 111, 196, 200, 144, 91, 48, 27, 10, 11, 1, 27, 150, 314, 335, 273, 168, 104, 54, 30 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Row sums = A000219, number of planar partitions of n starting with offset 1. /Q (1, 3, 6, 13, 24, 48,...).

LINKS

Table of n, a(n) for n=1..76.

FORMULA

Construct an array with rows = a, a*b, a*b*c,...; where a = [1, 1, 1,...], b = [1, 0, 2, 0, 3,...], c = [1, 0, 0, 3, 0, 0, 6,...], d = [1, 0, 0, 0, 4, 0, 0, 0, 10, 0, 0, 0, 20,...]...;etc, where rows converge to A000219: (1, 1, 3, 6, 13, 24,...). The triangle = finite differences of column terms starting from the top.

EXAMPLE

First few rows of the array =

1,...1,...1,...1,...1,...1,...; = a

1,...1,...3,...3,...6,...6,...; = a*b

1,...1,...3,...6,...9,..15,...; = a*b*c

1,...1,...3,...6,..13,..19,...; = a*b*c*d

1,...1,...3,...6,..13,..24,...; = a*b*c*d*e

...

...then taking finite differences from the top and discarding the first "1" /Q we obtain:

1;

1, 2;

1, 2, 3;

1, 5, 3, 4;

1, 5, 9, 4, 5;

1, 9, 15, 12, 5, 6;

1, 9, 24, 24, 15, 6, 7;

1, 14, 36, 46, 30, 18, 7, 8;

1, 14, 58, 70, 65, 36, 21, 8, 9;

1, 20, 76, 130, 110, 78, 42, 24, 9, 10;

1, 20, 111, 196, 200, 144, 91, 48, 27, 10, 11;

1, 27, 150, 314, 335, 273, 168, 104, 54, 30, 11, 12;

...

CROSSREFS

A000219

Sequence in context: A101391 A117704 A078032 * A008313 A232177 A111377

Adjacent sequences:  A162450 A162451 A162452 * A162454 A162455 A162456

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Jul 03 2009

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 18 11:56 EDT 2018. Contains 316321 sequences. (Running on oeis4.)