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 A274835 Number A(n,k) of set partitions of [n] such that the difference between each element and its block index is a multiple of k; square array A(n,k), n>=0, k>=0, read by antidiagonals. 10
 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 5, 1, 1, 1, 1, 2, 15, 1, 1, 1, 1, 1, 3, 52, 1, 1, 1, 1, 1, 2, 7, 203, 1, 1, 1, 1, 1, 1, 3, 14, 877, 1, 1, 1, 1, 1, 1, 2, 4, 39, 4140, 1, 1, 1, 1, 1, 1, 1, 3, 9, 95, 21147, 1, 1, 1, 1, 1, 1, 1, 2, 4, 18, 304, 115975, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 LINKS Alois P. Heinz, Antidiagonals n = 0..140, flattened Wikipedia, Partition of a set EXAMPLE A(3,0) = 1: 1|2|3. A(3,1) = 5: 123, 12|3, 13|2, 1|23, 1|2|3. A(5,2) = 7: 135|24, 13|24|5, 15|24|3, 1|24|35, 15|2|3|4, 1|2|35|4, 1|2|3|4|5. A(7,3) = 9: 147|25|36, 14|25|36|7, 17|25|36|4, 1|25|36|47, 17|2|36|4|5, 1|2|36|47|5, 17|2|3|4|5|6, 1|2|3|47|5|6, 1|2|3|4|5|6|7. Square array A(n,k) begins:   1,      1,   1,  1,  1, 1, 1, 1, 1, 1, 1, ...   1,      1,   1,  1,  1, 1, 1, 1, 1, 1, 1, ...   1,      2,   1,  1,  1, 1, 1, 1, 1, 1, 1, ...   1,      5,   2,  1,  1, 1, 1, 1, 1, 1, 1, ...   1,     15,   3,  2,  1, 1, 1, 1, 1, 1, 1, ...   1,     52,   7,  3,  2, 1, 1, 1, 1, 1, 1, ...   1,    203,  14,  4,  3, 2, 1, 1, 1, 1, 1, ...   1,    877,  39,  9,  4, 3, 2, 1, 1, 1, 1, ...   1,   4140,  95, 18,  5, 4, 3, 2, 1, 1, 1, ...   1,  21147, 304, 33, 11, 5, 4, 3, 2, 1, 1, ...   1, 115975, 865, 89, 22, 6, 5, 4, 3, 2, 1, ... MAPLE b:= proc(n, k, m, t) option remember; `if`(n=0, 1,      add(`if`(irem(j-t, k)=0, b(n-1, k, max(m, j),               irem(t+1, k)), 0), j=1..m+1))     end: A:= (n, k)-> `if`(k=0, 1, b(n, k, 0, 1)): seq(seq(A(n, d-n), n=0..d), d=0..14); MATHEMATICA b[n_, k_, m_, t_] := b[n, k, m, t] = If[n==0, 1, Sum[If[Mod[j-t, k]==0, b[n-1, k, Max[m, j], Mod[t+1, k]], 0], {j, 1, m+1}]]; A[n_, k_]:= If[k==0, 1, b[n, k, 0, 1]]; Table[A[n, d-n], {d, 0, 14}, {n, 0, d}] // Flatten (* Jean-François Alcover, Dec 18 2016, after Alois P. Heinz *) CROSSREFS Columns k=0-10 give: A000012, A000110, A274538, A274836, A274837, A274838, A274839, A274840, A274841, A274842, A274843. Main diagonal gives A000012. A(n,ceiling(n/2)) gives A008619. A(3n,n) gives A094002. Sequence in context: A333418 A212363 A212382 * A275069 A181937 A233836 Adjacent sequences:  A274832 A274833 A274834 * A274836 A274837 A274838 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Jul 08 2016 STATUS approved

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Last modified May 21 21:43 EDT 2022. Contains 353929 sequences. (Running on oeis4.)