cp's OEIS Frontend

A306318 Number of square twice-partitions of n.

%I A306318 #9 Feb 08 2019 22:07:13
%S A306318 1,1,1,1,2,2,4,5,10,12,19,24,39,49,73,104,151,212,317,443,638,936,
%T A306318 1296,1841,2635,3641,5069,7176,9884,13614,19113,26162,36603,50405,
%U A306318 70153,96176,135388,184753,257882,353587,494653,671992,934905,1272195,1762979,2389255
%N A306318 Number of square twice-partitions of n.
%C A306318 A twice partition of n is a sequence of integer partitions, one of each part in an integer partition of n. It is square if the number of parts is equal to the number of parts in each part.
%H A306318 Alois P. Heinz, <a href="/A306318/b306318.txt">Table of n, a(n) for n = 0..1000</a>
%e A306318 The a(10) = 19 square twice-partitions:
%e A306318   ((ten))  ((32)(32))  ((211)(111)(111))
%e A306318            ((32)(41))
%e A306318            ((33)(22))
%e A306318            ((33)(31))
%e A306318            ((41)(32))
%e A306318            ((41)(41))
%e A306318            ((42)(22))
%e A306318            ((42)(31))
%e A306318            ((43)(21))
%e A306318            ((44)(11))
%e A306318            ((51)(22))
%e A306318            ((51)(31))
%e A306318            ((52)(21))
%e A306318            ((53)(11))
%e A306318            ((61)(21))
%e A306318            ((62)(11))
%e A306318            ((71)(11))
%t A306318 Table[Sum[Length[Union@@(Tuples[IntegerPartitions[#,{k}]&/@#]&/@IntegerPartitions[n,{k}])],{k,0,Sqrt[n]}],{n,0,20}]
%Y A306318 Cf. A000219, A001970, A063834 (twice-partitions), A089299 (square plane partitions), A279787, A305551, A306017, A306319 (rectangular twice-partitions), A319066, A323429, A323531 (square partitions of partitions).
%K A306318 nonn
%O A306318 0,5
%A A306318 _Gus Wiseman_, Feb 07 2019