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Number of partitions of n into 3 parts whose largest part divides n.
1

%I #10 Feb 18 2023 20:28:14

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

%T 0,10,0,9,1,10,0,11,0,11,1,11,0,13,0,12,1,13,0,14,0,14,1,14,0,16,0,15,

%U 1,16,0,17,0,17,1,17,0,19,0,18,1,19,0,20,0,20,1,20,0,22,0

%N Number of partitions of n into 3 parts whose largest part divides n.

%H Antti Karttunen, <a href="/A348537/b348537.txt">Table of n, a(n) for n = 1..10480</a>

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} (1 - ceiling(n/(n-i-j)) + floor(n/(n-i-j))).

%t Array[Sum[Sum[(1 - Ceiling[#/(# - i - j)] + Floor[#/(# - i - j)]), {i, j, Floor[(# - j)/2]} ], {j, Floor[#/3]} ] &, 85] (* _Michael De Vlieger_, Oct 21 2021 *)

%o (PARI) A348537(n) = sum(j=1,(n\3), sum(i=j,((n-j)\2), (1 - ceil(n/(n-i-j)) + floor(n/(n-i-j))))); \\ _Antti Karttunen_, Feb 18 2023

%Y Cf. A069905.

%K nonn

%O 1,6

%A _Wesley Ivan Hurt_, Oct 21 2021