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 A240180 Number of partitions of n such that (least part) = (multiplicity of greatest part). 3
 0, 1, 0, 1, 3, 3, 5, 7, 12, 16, 24, 30, 45, 57, 81, 104, 143, 179, 243, 304, 399, 504, 650, 809, 1039, 1286, 1622, 2006, 2508, 3077, 3822, 4666, 5747, 6995, 8552, 10353, 12603, 15189, 18371, 22071, 26570, 31785, 38104, 45419, 54213, 64426, 76596, 90710 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Also the number of partitions p of n such that min(p) = min(conjugate(p)). Example:a(7) counts these 7 partitions: 61, 511, 421, 4111, 3211, 31111, 211111, of which the respective conjugates are 211111, 31111, 3211, 4111, 421, 511, 61. - Clark Kimberling, Apr 11 2014 LINKS Table of n, a(n) for n=0..47. FORMULA a(n) = A240179(n) - A240178(n), for n >= 0. a(n) + 2*A240178(n) = A000041(n) for n >= 0. EXAMPLE a(6) counts these 5 partitions: 51, 411, 321, 3111, 21111. MATHEMATICA z = 60; f[n_] := f[n] = IntegerPartitions[n]; Table[Count[f[n], p_ /; Min[p] < Count[p, Max[p]]], {n, 0, z}] (* A240178 *) Table[Count[f[n], p_ /; Min[p] <= Count[p, Max[p]]], {n, 0, z}] (* A240179 *) Table[Count[f[n], p_ /; Min[p] == Count[p, Max[p]]], {n, 0, z}] (* A240180 *) Table[Count[f[n], p_ /; Min[p] > Count[p, Max[p]]], {n, 0, z}] (* A240178, n>0 *) Table[Count[f[n], p_ /; Min[p] >= Count[p, Max[p]]], {n, 0, z}] (* A240179, n>0 *) CROSSREFS Cf. A240178, A240179, A000041. Sequence in context: A001588 A107029 A352912 * A169942 A215777 A147095 Adjacent sequences: A240177 A240178 A240179 * A240181 A240182 A240183 KEYWORD nonn,easy AUTHOR Clark Kimberling, Apr 02 2014 STATUS approved

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Last modified June 2 20:13 EDT 2023. Contains 363100 sequences. (Running on oeis4.)