cp's OEIS Frontend

A386361 Number of partitions of n such that the least part occurs exactly (1/4)*(number of parts) times.

%I A386361 #9 Jul 19 2025 10:11:07
%S A386361 0,0,0,0,0,0,1,1,2,3,5,6,9,12,16,20,26,32,41,50,62,76,93,112,136,164,
%T A386361 197,237,283,339,403,480,569,676,799,945,1113,1314,1543,1815,2125,
%U A386361 2494,2912,3407,3970,4632,5384,6266,7268,8438,9766,11310,13063,15097,17402
%N A386361 Number of partitions of n such that the least part occurs exactly (1/4)*(number of parts) times.
%o A386361 (Ruby)
%o A386361 def partition(n, min, max)
%o A386361   return [[]] if n == 0
%o A386361   [max, n].min.downto(min).flat_map{|i| partition(n - i, min, i).map{|rest| [i, *rest]}}
%o A386361 end
%o A386361 def A(n, k)
%o A386361   cnt = 0
%o A386361   partition(n, 1, n).each{|ary|
%o A386361     cnt += 1 if k * ary.count(ary.min) == ary.size
%o A386361   }
%o A386361   cnt
%o A386361 end
%o A386361 def A386361(n)
%o A386361   (1..n).map{|i| A(i, 4)}
%o A386361 end
%o A386361 p A386361(40)
%Y A386361 Cf. A000005, A239497, A386360.
%Y A386361 Cf. A237826.
%K A386361 nonn
%O A386361 1,9
%A A386361 _Seiichi Manyama_, Jul 19 2025