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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 11 2019
STATUS
approved