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

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!)
 A325187 Number of integer partitions of n such that the upper-left square of the Young diagram has strictly greater graph-distance from the lower-right boundary than any other square. 6
 1, 0, 1, 3, 3, 5, 9, 14, 20, 26, 38, 53, 75, 101, 132, 175, 229, 301, 394, 509, 650, 826, 1043, 1315, 1656, 2074, 2590, 3218, 3975, 4896, 6008, 7361, 8989, 10960, 13323, 16159, 19531, 23553, 28323, 34002, 40723, 48694, 58115, 69249, 82350, 97766, 115832 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS The k-th part of the origin-to-boundary partition of a Young diagram is the number of squares graph-distance k from the lower-right boundary. The sequence gives the number of integer partitions of n whose Young diagram has last part of its origin-to-boundary partition equal to 1. The Heinz numbers of these partitions are given by A325185. LINKS Eric Weisstein's World of Mathematics, Graph Distance. EXAMPLE The a(1) = 1 through a(8) = 14 partitions:   (1)  (21)  (22)   (41)    (51)     (61)      (71)              (31)   (311)   (321)    (322)     (332)              (211)  (2111)  (411)    (331)     (422)                             (3111)   (421)     (431)                             (21111)  (511)     (521)                                      (3211)    (611)                                      (4111)    (3221)                                      (31111)   (3311)                                      (211111)  (4211)                                                (5111)                                                (32111)                                                (41111)                                                (311111)                                                (2111111) MATHEMATICA otb[ptn_]:=Min@@MapIndexed[#1+#2[[1]]-1&, Append[ptn, 0]]; Table[Length[Select[IntegerPartitions[n], otb[#]>otb[Rest[#]]&&otb[#]>otb[DeleteCases[#-1, 0]]&]], {n, 30}] CROSSREFS Cf. A000245, A188674, A325165, A325169, A325183, A325184, A325185, A325187, A325190, A325191. Sequence in context: A325849 A104220 A321986 * A209083 A137202 A146926 Adjacent sequences:  A325184 A325185 A325186 * A325188 A325189 A325190 KEYWORD nonn AUTHOR Gus Wiseman, Apr 11 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.

Last modified January 20 23:29 EST 2020. Contains 331104 sequences. (Running on oeis4.)