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 A241742 Number of partitions p of n such that (number of numbers in p of form 3k+2) > (number of numbers in p of form 3k). 3
 0, 0, 1, 1, 2, 3, 5, 6, 9, 12, 18, 22, 31, 41, 54, 70, 95, 120, 156, 202, 259, 325, 418, 524, 659, 826, 1032, 1274, 1581, 1949, 2397, 2932, 3592, 4367, 5307, 6430, 7783, 9370, 11288, 13550, 16233, 19399, 23179, 27579, 32812, 38955, 46155, 54572, 64524, 76051 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Each number in p is counted once, regardless of its multiplicity. LINKS FORMULA a(n) + A241740(n) + A241841(n) = A000041(n) for n >= 0. EXAMPLE a(8) counts these 9 partitions:  8, 521, 5111, 422, 4211, 2222, 22211, 221111, 2111111. MATHEMATICA z = 40; f[n_] := f[n] = IntegerPartitions[n]; s[k_, p_] := Count[Mod[DeleteDuplicates[p], 3], k]; Table[Count[f[n], p_ /; s[2, p] < s[0, p]], {n, 0, z}]  (* A241740 *) Table[Count[f[n], p_ /; s[2, p] == s[0, p]], {n, 0, z}] (* A241741 *) Table[Count[f[n], p_ /; s[2, p] > s[0, p]], {n, 0, z}]  (* A241742 *) CROSSREFS Cf. A241737, A241740, A241741, A241743. Sequence in context: A035948 A258939 A244747 * A212584 A166048 A240306 Adjacent sequences:  A241739 A241740 A241741 * A241743 A241744 A241745 KEYWORD nonn,easy AUTHOR Clark Kimberling, Apr 28 2014 STATUS approved

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Last modified June 17 19:10 EDT 2019. Contains 324198 sequences. (Running on oeis4.)