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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

Alois P. Heinz, Table of n, a(n) for n = 0..1000

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

Cf. A241737, A241740, A241744, A241745.

Sequence in context: A261205 A036451 A297216 * A321729 A180652 A046682

Adjacent sequences:  A241740 A241741 A241742 * A241744 A241745 A241746

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 28 2014

STATUS

approved

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Last modified November 11 16:07 EST 2019. Contains 329019 sequences. (Running on oeis4.)