login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A325232 Number of integer partitions (of any nonnegative integer) whose sum minus the lesser of their maximum part and their number of parts is n. 8
2, 3, 6, 10, 18, 27, 44, 64, 97, 138, 200, 276, 390, 528, 724, 968, 1301, 1712, 2266, 2946, 3842, 4947, 6372, 8122, 10362, 13094, 16544, 20754, 26010, 32392, 40308, 49876, 61648, 75845, 93178, 114006, 139308, 169586, 206158, 249814, 302267, 364664, 439330 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Giovanni Resta, Table of n, a(n) for n = 0..75

FindStat, St000533: The maximal number of non-attacking rooks on a Ferrers shape

FORMULA

For n > 0, a(n) = Sum_{k > 0} A325227(n + k, k).

EXAMPLE

The a(0) = 1 through a(4) = 18 partitions:

  ()   (2)   (3)    (4)     (5)

  (1)  (11)  (22)   (32)    (33)

       (21)  (31)   (41)    (42)

             (111)  (221)   (51)

             (211)  (321)   (222)

             (311)  (411)   (322)

                    (1111)  (331)

                    (2111)  (421)

                    (3111)  (511)

                    (4111)  (2211)

                            (3211)

                            (4211)

                            (5111)

                            (11111)

                            (21111)

                            (31111)

                            (41111)

                            (51111)

MATHEMATICA

nn=30;

mindif[ptn_]:=If[ptn=={}, 0, Total[ptn]-Min[Length[ptn], Max[ptn]]];

allip=Array[IntegerPartitions, 2*nn+2, 0, Join];

Table[Length[Select[allip, mindif[#]==n&]], {n, 0, nn}]

CROSSREFS

Number of times n appears in A325224.

Cf. A051924, A257541, A263297, A325193, A325194, A325224, A325225, A325227.

Sequence in context: A193200 A026779 A081028 * A208479 A065441 A075531

Adjacent sequences:  A325229 A325230 A325231 * A325233 A325234 A325235

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 13 2019

EXTENSIONS

More terms from Giovanni Resta, Apr 15 2019

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 8 20:37 EST 2021. Contains 349596 sequences. (Running on oeis4.)