A340390 Number of partitions of n into 4 parts such that the largest part is 3 times the smallest part.

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, 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, 16, 19, 17, 20, 19, 22, 20, 23, 21, 24, 22, 25, 23, 27, 25, 28, 26, 29, 27, 31, 29

Offset

0,9

Links

David A. Corneth, Table of n, a(n) for n = 0..9999

Index entries for sequences related to partitions

Formula

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.

Mathematica

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}]
Table[Count[IntegerPartitions[n, {4}], _?(#[[1]]==3#[[4]]&)], {n, 0, 80}] (* Harvey P. Dale, Mar 25 2021 *)

Prog

(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

Crossrefs

Sequence in context: A025897 A029421 A156749 * A325280 A039803 A360118

Adjacent sequences: A340387 A340388 A340389 * A340391 A340392 A340393

Keyword

nonn

Author

Wesley Ivan Hurt, Jan 06 2021

Status

approved