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%I #12 Mar 27 2021 23:47:44
%S 0,0,0,0,0,0,1,1,2,1,1,0,1,1,2,2,3,2,3,2,3,2,3,3,5,4,5,4,5,4,6,5,7,6,
%T 7,6,8,7,9,8,10,8,10,9,11,10,12,11,14,12,14,12,14,13,16,15,18,16,18,
%U 16,19,17,20,19,22,20,23,21,24,22,25,23,27,25,28,26,29,27,31,29
%N Number of partitions of n into 4 parts such that the largest part is 3 times the smallest part.
%H David A. Corneth, <a href="/A340390/b340390.txt">Table of n, a(n) for n = 0..9999</a>
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} [4*k = n-i-j], where [ ] is the Iverson bracket.
%t Table[Sum[Sum[Sum[KroneckerDelta[4 k, n - i - j], {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 80}]
%t Table[Count[IntegerPartitions[n,{4}],_?(#[[1]]==3#[[4]]&)],{n,0,80}] (* _Harvey P. Dale_, Mar 25 2021 *)
%o (PARI) first(n) = {n--; my(res = vector(n)); for(i = 1, n \ 6, for(j = 6*i, min(10*i, n), res[j] += 1 + min(abs(j - 6*i), abs(j - 10*i))\2 ) ); concat(0, res) } \\ _David A. Corneth_, Mar 25 2021
%K nonn
%O 0,9
%A _Wesley Ivan Hurt_, Jan 06 2021
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