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 A238406 Number T(n,k) of partitions of n into k parts such that every i-th smallest part (counted with multiplicity) is different from i; triangle T(n,k), n>=0, 0<=k<=floor((sqrt(9+8*n)-3)/2) read by rows. 10
 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 2, 0, 1, 2, 0, 1, 3, 0, 1, 3, 1, 0, 1, 4, 3, 0, 1, 4, 4, 0, 1, 5, 6, 0, 1, 5, 7, 0, 1, 6, 9, 1, 0, 1, 6, 11, 4, 0, 1, 7, 13, 7, 0, 1, 7, 15, 11, 0, 1, 8, 18, 15, 0, 1, 8, 20, 19, 0, 1, 9, 23, 25, 1, 0, 1, 9, 26, 30, 5 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,14 LINKS Alois P. Heinz, Rows n = 0..500, flattened EXAMPLE T(10,1) = 1: [10]. T(10,2) = 4: [5,5], [4,6], [3,7], [2,8]. T(10,3) = 3: [3,3,4], [2,4,4], [2,3,5]. Triangle T(n,k) begins: 1; 0; 0, 1; 0, 1; 0, 1; 0, 1, 1; 0, 1, 2; 0, 1, 2; 0, 1, 3; 0, 1, 3, 1; 0, 1, 4, 3; 0, 1, 4, 4; 0, 1, 5, 6; 0, 1, 5, 7; 0, 1, 6, 9, 1; ... MAPLE b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, b(n, i-1)+`if`(i>n, 0, (p-> expand( x*(p-coeff(p, x, i-1)*x^(i-1))))(b(n-i, i))))) end: T:= n-> (p-> seq(coeff(p, x, i), i=0..max(0, degree(p))))(b(n\$2)): seq(T(n), n=0..30); MATHEMATICA b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, b[n, i-1] + If[i>n, 0, Function[p, Expand[x*(p - Coefficient[p, x, i-1]*x^(i-1))]][b[n-i, i]]]] ]; T[n_] := Function[p, Table[Coefficient[p, x, i], {i, 0, Max[0, Exponent[p, x]]}]][b[n, n]]; Table[T[n], {n, 0, 30}] // Flatten (* Jean-François Alcover, Feb 08 2017, translated from Maple *) CROSSREFS Columns k=0-10 give: A000007, A000012 (for n>1), A004526(n-2) (for n>4), A244239, A244240, A244241, A244242, A244243, A244244, A244245, A244246. Row sums give A238394. Cf. A052146. Sequence in context: A163325 A105186 A328346 * A058709 A025842 A141100 Adjacent sequences: A238403 A238404 A238405 * A238407 A238408 A238409 KEYWORD nonn,tabf,look AUTHOR Alois P. Heinz, Feb 26 2014 STATUS approved

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Last modified August 15 13:43 EDT 2024. Contains 375173 sequences. (Running on oeis4.)