|
|
A321016
|
|
Triangle read by rows: number of partitions of n into distinct and consecutive parts with largest part k (n >= 1, 1 <= k <= n)..
|
|
0
|
|
|
1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
EXAMPLE
|
Triangle begins:
[1]
[0, 1]
[0, 1, 1]
[0, 0, 0, 1]
[0, 0, 1, 0, 1]
[0, 0, 1, 0, 0, 1]
[0, 0, 0, 1, 0, 0, 1]
[0, 0, 0, 0, 0, 0, 0, 1]
[0, 0, 0, 1, 1, 0, 0, 0, 1]
[0, 0, 0, 1, 0, 0, 0, 0, 0, 1]
[0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1]
[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1]
[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1]
[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1]
[0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1]
...
|
|
MAPLE
|
with(combinat);
f2:=proc(n) local i, j, p, t0, t1, t2;
t0:=Array(1..n, 0); t1:=partition(n); p:=numbpart(n);
for i from 1 to p do t2:=t1[i];
if nops(convert(t2, set))=nops(t2) then
# now have a partition t2 of n into distinct parts
gd:=1;
if nops(t2)>1 then
for j from 1 to nops(t2)-1 do if t2[j+1]-t2[j]>1 then gd:=-1; fi;
od; fi;
# now have a partition t2 of n into distinct consecutive parts
if gd=1 then t0[t2[-1]]:=t0[t2[-1]]+1; fi;
fi;
od:
[seq(t0[j], j=1..n)];
end proc;
for n from 1 to 15 do lprint(f2(n)) od:
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|