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 A167930 Number of partitions of n in which some but not all parts are equal. 3
 0, 0, 0, 0, 1, 3, 4, 9, 13, 20, 29, 43, 57, 82, 110, 146, 195, 258, 334, 435, 558, 713, 910, 1150, 1446, 1814, 2268, 2815, 3491, 4308, 5301, 6501, 7954, 9692, 11795, 14295, 17301, 20876, 25148, 30200, 36218, 43322, 51741, 61650, 73354 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 LINKS FORMULA a(n) = A047967(n) - A032741(n). a(n) = A000041(n) - A000009(n) - A032741(n). a(0) = 0: For n>0, a(n) = A000041(n) - A000009(n) - A000005(n) + 1. EXAMPLE The partitions of 6 are: 6 ....................... All parts are distinct. 5 + 1 ................... All parts are distinct. 4 + 2 ................... All parts are distinct. 4 + 1 + 1 ............... Only some parts are equal ...... (1). 3 + 3 ................... All parts are equal. 3 + 2 + 1 ............... All parts are distinct. 3 + 1 + 1 + 1 ........... Only some parts are equal ...... (2). 2 + 2 + 2 ............... All parts are equal. 2 + 2 + 1 + 1 ........... Only some parts are equal ...... (3). 2 + 1 + 1 + 1 + 1 ....... Only some parts are equal ...... (4). 1 + 1 + 1 + 1 + 1 + 1 ... All parts are equal. Then a(6) = 4. CROSSREFS Cf. A000005, A000009, A000041, A000065, A032741, A047967, A111133, A134400, A135010, A138121, A167931, A167932, A167933. Sequence in context: A116552 A339996 A225288 * A326981 A124285 A131326 Adjacent sequences:  A167927 A167928 A167929 * A167931 A167932 A167933 KEYWORD nonn AUTHOR Omar E. Pol, Nov 15 2009 EXTENSIONS Edited by Omar E. Pol, Nov 16 2009 More terms from Max Alekseyev, May 02 2011 STATUS approved

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Last modified June 12 08:13 EDT 2021. Contains 344943 sequences. (Running on oeis4.)