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A340390
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Number of partitions of n into 4 parts such that the largest part is 3 times the smallest part.
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1
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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
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OFFSET
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0,9
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LINKS
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David A. Corneth, Table of n, a(n) for n = 0..9999
Index entries for sequences related to partitions
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FORMULA
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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.
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Sequence in context: A025897 A029421 A156749 * A325280 A039803 A360118
Adjacent sequences: A340387 A340388 A340389 * A340391 A340392 A340393
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KEYWORD
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nonn
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AUTHOR
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Wesley Ivan Hurt, Jan 06 2021
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STATUS
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approved
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