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A145573 Characteristic partition array for partitions without part 1. 3


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

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

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

%N Characteristic partition array for partitions without part 1.

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

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

%C The entries of row n are grouped together for 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 A145574.

%H W. Lang and M. Sjodahl <a href="/A145573/a145573.txt">First 10 rows of the array and row sums.</a>

%F As array: a(n,k)=1 if the k-th partition of n in A-St order has no part 1, 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 [0],[1,0],[1,0,0],[1,0,1,0,0],[1,0,1,0,0,0,0],...

%e a(4,3) = a(1+2+3+3) = a(9) = 1 because a(4,3) belongs to the partition [2^2]=[2,2] of n=4 which has no part 1.

%Y Cf. A145574 (without zeros). A002865 (row sums).

%K nonn,easy,tabf

%O 1,1

%A _Wolfdieter Lang_ and Malin Sjodahl, Mar 06 2009

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Last modified October 22 09:31 EDT 2019. Contains 328315 sequences. (Running on oeis4.)