A187446 - OEIS

%I #12 Dec 13 2015 01:09:20

%S 0,1,2,2,3,3,4,4,5,3,4,5,6,4,5,6,7,5,6,7,8,5,6,6,7,8,9,4,6,7,7,8,9,10,

%T 5,7,8,8,9,10,11,6,6,7,8,8,9,9,10,11,12,6,7,7,8,9,9,10,10,11,12,13,7,

%U 8,8,9,10,10,11,11,12

%N Number of parts of the multiset repetition class defining partition (n,k) in Abramowitz-Stegun order.

%C For the Abramowitz-Stegun (A-St) order of partitions see A036036.

%C For the first 87 multiset defining partitions in A-St order see a link under A176725.

%C This sequence is an irregular array with row length sequence A007294(n).

%F Sum(en[j],j=1..M(n)]), with the n-th multiset defining partition in A-St order written as (1^en[1],2^en[2],...,M^en[M]), with M=M(n) its largest part, and positive, nonincreasing exponents en[1]>=en[2]>=...>=en[M]>=1. a(0)=0 from the empty partition defining the empty multiset.

%e Read as array:

%e 0;

%e 1;

%e 2;

%e 2,3;

%e 3,4;

%e 4,5;

%e 3,4,5,6;

%e 4,5,6,7;

%e 5,6,7,8;

%e 5,6,6,7,8,9;

%e 4, 6, 7, 7, 8, 9, 10;

%e ...,

%e linking (for row number n>=0) to the number of parts of the corresponding partitions of n.

%Y Cf. A176725, A187447.

%K nonn,easy,tabf

%O 0,3

%A _Wolfdieter Lang_, Mar 14 2011