

A145361


Characteristic partition array for partitions with parts 1 and 2 only.


3



1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET

1,1


COMMENTS

Each partition of n, ordered like in AbramowitzStegun (ASt order; for the reference see A134278), is mapped to 1 if the partition has parts 1 or 2 only and to 0 otherwise.
First member (K=1) in the family M31hat(K) of partition number arrays.
The sequence of row lengths is A000041 (partition numbers) [1, 2, 3, 5, 7, 11, 15, 22, 30, 42,...].
If M31hat(1;n,k) is summed over those k numerating partitions with fixed number of parts m one obtains the unsigned triangle S1hat(1):= A145362 .


LINKS



FORMULA

a(n,k) = product(S1(1;j,1)^e(n,k,j),j=1..n) with S1(1;n,1) = A008279(1,n1) = [1,1,0,0,0,...], n>=1 and the exponent e(n,k,j) of j in the kth partition of n in the ASt ordering of the partitions of n.


EXAMPLE

[1];[1,1];[0,1,1];[0,0,1,1,1];[0,0,0,0,1,1,1];...
a(4,3)= 1 = S1(1;2,1)^2. The relevant partition of 4 is (2^2).


CROSSREFS



KEYWORD

nonn,easy,tabf


AUTHOR



STATUS

approved



