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 A083751 Number of partitions of n into >= 2 parts and with minimum part >= 2. 16
 0, 0, 0, 1, 1, 3, 3, 6, 7, 11, 13, 20, 23, 33, 40, 54, 65, 87, 104, 136, 164, 209, 252, 319, 382, 477, 573, 707, 846, 1038, 1237, 1506, 1793, 2166, 2572, 3093, 3659, 4377, 5169, 6152, 7244, 8590, 10086, 11913, 13958, 16423, 19195, 22518, 26251, 30700, 35716 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS Also number of partitions of n such that the largest part is at least 2 and occurs at least twice. Example: a(6)=3 because we have [3,3],[2,2,2] and [2,2,1,1]. - Emeric Deutsch, Mar 29 2006 Also number of partitions of n that contain emergent parts (Cf. A182699). - Omar E. Pol, Oct 21 2011 Also number of regions in the last section of the set of partitions of n that do not contain 1 as a part (cf. A187219). - Omar E. Pol, Mar 04 2012 Schneider calls these "nuclear partitions" and gives a remarkable formula relating a(n), the number of partitions of n, and a sum over the two greatest parts of each such partition. - Charles R Greathouse IV, Dec 04 2019 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..1000 Robert Schneider, Nuclear partitions and a formula for p(n), arXiv:1912.00575 [math.NT], 2019. FORMULA a(n) = A000041(n) - A000041(n-1) - 1, n > 1. - Vladeta Jovovic, Jun 18 2003 G.f.: Sum_{j>=2} x^(2j)/Product_{i=1..j} (1-x^i). - Emeric Deutsch, Mar 29 2006 a(n) = A002865(n) - 1, n > 1. - Omar E. Pol, Oct 21 2011 a(n) = A187219(n) - 1. - Omar E. Pol, Mar 04 2012 EXAMPLE a(6) = 3, as 6 = 2+4 = 3+3 = 2+2+2. a(6) = 3 because 6 = 2+4 = 3+3 = 2+2+2. MAPLE g:=sum(x^(2*j)/product(1-x^i, i=1..j), j=2..50): gser:=series(g, x=0, 55): seq(coeff(gser, x, n), n=1..51); # Emeric Deutsch, Mar 29 2006 MATHEMATICA Drop[CoefficientList[Series[1/Product[(1-x^k)^1, {k, 2, 50}], {x, 0, 50}], x]-1, 2] (* or *) Table[Count[IntegerPartitions[n], q_List /; Length[q] > 1 && Min[q] >= 2 ], {n, 24}] CROSSREFS Cf. A053445, A072380, A008483, A026796, A035989, A036000, A002865, A081094. Cf. A002865. First differences of A000094. Sequence in context: A211541 A026926 A332557 * A034401 A240449 A088571 Adjacent sequences:  A083748 A083749 A083750 * A083752 A083753 A083754 KEYWORD nonn AUTHOR Jon Perry, Jun 17 2003 EXTENSIONS More terms from Vladeta Jovovic and Wouter Meeussen, Jun 18 2003 Description corrected by James A. Sellers, Jun 21 2003 STATUS approved

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Last modified September 21 03:13 EDT 2020. Contains 337266 sequences. (Running on oeis4.)