login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons 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!)
A116647 Triangle of number of partitions that fit in an n X n box (but not in an (n-1) X (n-1) box) with Durfee square k. 2
1, 3, 1, 5, 8, 1, 7, 27, 15, 1, 9, 64, 84, 24, 1, 11, 125, 300, 200, 35, 1, 13, 216, 825, 1000, 405, 48, 1, 15, 343, 1911, 3675, 2695, 735, 63, 1, 17, 512, 3920, 10976, 12740, 6272, 1232, 80, 1, 19, 729, 7344, 28224, 47628, 37044, 13104, 1944, 99, 1, 21, 1000, 12825 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Eric Weisstein's World of Mathematics, Durfee Square.

FORMULA

T(n,k) = binomial(n,k)^2 - binomial(n-1,k)^2.

EXAMPLE

Triangle begins

   1;

   3,   1;

   5,   8,   1;

   7,  27,  15,   1;

   9,  64,  84,  24,   1;

  11, 125, 300, 200,  35,   1;

MATHEMATICA

Table[Binomial[n, k]^2 - Binomial[n - 1, k], {n, 1, 10}, {k, 1, n}] // Flatten (* G. C. Greubel, Nov 20 2017 *)

PROG

(PARI) for(n=1, 10, for(k=0, n, print1(binomial(n, k)^2 - binomial(n-1, k)^2, ", "))) \\ G. C. Greubel, Nov 20 2017

CROSSREFS

Cf. A008459; row sums A051924.

Sequence in context: A038738 A210741 A208760 * A063858 A209831 A284367

Adjacent sequences:  A116644 A116645 A116646 * A116648 A116649 A116650

KEYWORD

easy,nonn,tabl

AUTHOR

Franklin T. Adams-Watters, Feb 20 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 16 09:13 EST 2021. Contains 340204 sequences. (Running on oeis4.)