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 A187219 Number of partitions of n that do not contain parts less than the smallest part of the partitions of n-1. 54
 1, 1, 1, 2, 2, 4, 4, 7, 8, 12, 14, 21, 24, 34, 41, 55, 66, 88, 105, 137, 165, 210, 253, 320, 383, 478, 574, 708, 847, 1039, 1238, 1507, 1794, 2167, 2573, 3094, 3660, 4378, 5170, 6153, 7245, 8591, 10087, 11914, 13959, 16424, 19196, 22519, 26252, 30701, 35717 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Essentially the same as A002865, but here a(1) = 1 not 0. Also number of regions in the last section of the set of partitions of n. Also number of partitions of n+k that are formed by k+1 sections, k >= 0 (Cf. A194799). - Omar E. Pol, Jan 30 2012 For the definition of region see A206437. - Omar E. Pol, Aug 13 2013 Partial sums give A000041, n >= 1. - Omar E. Pol, Sep 04 2013 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Omar E. Pol, Illustration of the seven regions of 5 FORMULA a(n) = A083751(n) + 1. - Omar E. Pol, Mar 04 2012 a(n) = A002865(n), if n >= 2. - Omar E. Pol, Aug 13 2013 EXAMPLE From Omar E. Pol, Aug 13 2013: (Start) Illustration of initial terms as number of regions: .                                           _ _ _ _ _ _ .                                          |_ _ _      | .                                          |_ _ _|_    | .                                          |_ _    |   | .                               _ _ _ _ _  |_ _|_ _|_  | .                              |_ _ _    |           | | .                     _ _ _ _  |_ _ _|_  |           | | .                    |_ _    |         | |           | | .             _ _ _  |_ _|_  |         | |           | | .       _ _  |_ _  |       | |         | |           | | .   _  |_  |     | |       | |         | |           | | .  |_|   |_|     |_|       |_|         |_|           |_| . .   1     1       1         2           2             4 . (End) MATHEMATICA Join[{1}, Drop[CoefficientList[Series[1 / Product[(1 - x^k)^1, {k, 2, 50}], {x, 0, 50}], x], 2]] (* Vincenzo Librandi, Feb 15 2018 *) CROSSREFS Cf. A000041, A002865, A083751, A135010, A186114, A193870, A206437, A225600, A225610. Sequence in context: A036000 A002865 A085811 * A317785 A014810 A318771 Adjacent sequences:  A187216 A187217 A187218 * A187220 A187221 A187222 KEYWORD nonn,less AUTHOR Omar E. Pol, Dec 09 2011 EXTENSIONS Better definition from Omar E. Pol, Sep 04 2013 STATUS approved

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Last modified December 6 14:15 EST 2019. Contains 329806 sequences. (Running on oeis4.)