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 A276429 Number of partitions of n containing no part i of multiplicity i. 18
 1, 0, 2, 2, 3, 5, 8, 9, 16, 19, 29, 36, 53, 65, 92, 115, 154, 195, 257, 318, 419, 516, 663, 821, 1039, 1277, 1606, 1963, 2441, 2978, 3675, 4454, 5469, 6603, 8043, 9688, 11732, 14066, 16963, 20260, 24310, 28953, 34586, 41047, 48857, 57802, 68528, 80862, 95534, 112388, 132391 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The Heinz numbers of these partitions are given by A325130. - Gus Wiseman, Apr 02 2019 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..12782 (terms 0..5000 from Alois P. Heinz) FORMULA a(n) = A276427(n,0). G.f.: g(x) = Product_{i>=1} (1/(1-x^i) - x^{i^2}). EXAMPLE a(4) = 3 because we have [1,1,1,1], [1,1,2], and [4]; the partitions [1,3], [2,2] do not qualify. From Gus Wiseman, Apr 02 2019: (Start) The a(2) = 2 through a(7) = 9 partitions: (2) (3) (4) (5) (6) (7) (11) (111) (211) (32) (33) (43) (1111) (311) (42) (52) (2111) (222) (511) (11111) (411) (3211) (3111) (4111) (21111) (31111) (111111) (211111) (1111111) (End) MAPLE g := product(1/(1-x^i)-x^(i^2), i = 1 .. 100): gser := series(g, x = 0, 53): seq(coeff(gser, x, n), n = 0 .. 50); # second Maple program: b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(`if`(i=j, 0, b(n-i*j, i-1)), j=0..n/i))) end: a:= n-> b(n\$2): seq(a(n), n=0..60); # Alois P. Heinz, Sep 19 2016 MATHEMATICA b[n_, i_] := b[n, i] = Expand[If[n == 0, 1, If[i < 1, 0, Sum[If[i == j, x, 1]*b[n - i*j, i - 1], {j, 0, n/i}]]]]; T[n_] := Function[p, Table[Coefficient[p, x, i], {i, 0, Exponent[p, x]}]][b[n, n]]; Table[T[n][[1]], {n, 0, 60}] (* Jean-François Alcover, Nov 28 2016 after Alois P. Heinz's Maple code for A276427 *) Table[Length[Select[IntegerPartitions[n], And@@Table[Count[#, i]!=i, {i, Union[#]}]&]], {n, 0, 30}] (* Gus Wiseman, Apr 02 2019 *) CROSSREFS Cf. A052335, A087153, A114639, A115584, A117144, A276427, A324572, A325130, A325131, A336269. Sequence in context: A114990 A241421 A157176 * A111181 A267419 A076777 Adjacent sequences: A276426 A276427 A276428 * A276430 A276431 A276432 KEYWORD nonn AUTHOR Emeric Deutsch, Sep 19 2016 STATUS approved

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Last modified March 29 17:51 EDT 2023. Contains 361599 sequences. (Running on oeis4.)