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A241743 Number of partitions p of n such that (number of numbers in p of form 3k) < (number of numbers in p of form 3k+1). 9
0, 1, 1, 2, 3, 4, 6, 8, 12, 16, 21, 30, 40, 52, 72, 91, 121, 159, 202, 260, 335, 421, 535, 674, 840, 1052, 1304, 1614, 1996, 2451, 3002, 3674, 4468, 5442, 6592, 7971, 9624, 11584, 13898, 16691, 19947, 23823, 28410, 33782, 40113, 47610, 56302, 66572, 78569 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
Each number in p is counted once, regardless of its multiplicity.
LINKS
FORMULA
a(n) + A241744(n) + A241845(n) = A000041(n) for n >= 0.
EXAMPLE
a(8) counts these 12 partitions: 71, 521, 5111, 44, 431, 422, 4211, 41111, 22211, 221111, 2111111, 11111111.
MATHEMATICA
z = 40; f[n_] := f[n] = IntegerPartitions[n]; s[k_, p_] := Count[Mod[DeleteDuplicates[p], 3], k];
Table[Count[f[n], p_ /; s[0, p] < s[2, p]], {n, 0, z}] (* A241743 *)
Table[Count[f[n], p_ /; s[0, p] == s[1, p]], {n, 0, z}] (* A241744 *)
Table[Count[f[n], p_ /; s[0, p] > s[1, p]], {n, 0, z}] (* A241745 *)
CROSSREFS
Sequence in context: A261205 A036451 A297216 * A321729 A180652 A046682
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 28 2014
STATUS
approved

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Last modified April 15 14:58 EDT 2024. Contains 371692 sequences. (Running on oeis4.)