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A145575 Characteristic partition array for partitions with distinct parts. 1


%S 1,1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0,0,0,0,1,1,1,1,0,

%T 1,0,0,0,0,0,0,0,0,0,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,

%U 1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,0,0,1,1

%N Characteristic partition array for partitions with distinct parts.

%C The partitions are ordered according to Abramowitz-Stegun (A-St order). See e.g. A036040 for the reference, pp. 831-2.

%C Partitions with distinct parts could be called fermionic partitions, because the places 1,...,n for the possible parts are either empty or once occupied.

%C The row lengths of this array are p(n)=A000041(n) (number of partitions of n).

%C The entries of row n belong to partitions with rising parts number m from 1 to n. The number of partitions of n with m parts is p(n,m)= A008284(n,m), m=1..n, n>=1.

%C For the array without zeros see A008289.

%H Wolfdieter Lang, <a href="/A145575/a145575.pdf">First 10 rows of the array.</a>

%F As array: a(n,k)=1 if the k-th partition of n in A-St order has distinct parts, and a(n,k)=0 else.

%F Translated into the sequence a(m) entry: a(n,k) = a(sum(p(k),k=1..n)+k).

%e [1];[1,0];[1,1,0];[1,1,0,0,0];[1,1,1,0,0,0,0];...

%Y Cf. A000009 (row sums).

%K nonn,easy,tabf

%O 1,1

%A _Wolfdieter Lang_, Mar 06 2009

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Last modified October 14 18:28 EDT 2019. Contains 328022 sequences. (Running on oeis4.)