A321016 - OEIS

A321016

Triangle read by rows: number of partitions of n into distinct and consecutive parts with largest part k (n >= 1, 1 <= k <= n)..

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

COMMENTS

Suggested by A321440.

LINKS

Table of n, a(n) for n=1..120.

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

Row sums are A001227.

Cf. A321440.

Sequence in context: A077052 A133566 A185907 * A077051 A115955 A106344

Adjacent sequences: A321013 A321014 A321015 * A321017 A321018 A321019

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Nov 09 2018

STATUS

approved