A357354 - OEIS

%I #14 Sep 25 2022 14:50:21

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

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

%U 0,0,1,1,0,0,1,1,0,0,3,1,0,2,0,0,1,1,1

%N Number of partitions of n into distinct positive squares such that the number of parts is a square.

%H Alois P. Heinz, <a href="/A357354/b357354.txt">Table of n, a(n) for n = 0..20000</a>

%e a(30) = 1 because we have [16,9,4,1].

%e a(78) = 3: [36,25,16,1], [49,16,9,4], [64,9,4,1].

%p b:= proc(n, i, t) option remember; `if`(n=0,

%p      `if`(issqr(t), 1, 0), `if`(n>i*(i+1)*(2*i+1)/6, 0,

%p      `if`(i^2>n, 0, b(n-i^2, i-1, t+1))+b(n, i-1, t)))

%p     end:

%p a:= n-> b(n, isqrt(n), 0):

%p seq(a(n), n=0..100);  # _Alois P. Heinz_, Sep 25 2022

%Y Cf. A000290, A033461, A045450, A089333, A357352.

%K nonn

%O 0,79

%A _Ilya Gutkovskiy_, Sep 25 2022