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 A071201 Array A(n,k) read by antidiagonals giving number of paths up and right from (0,0) to (n,k) where x/y<=n/k. 6
 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 3, 5, 3, 1, 1, 3, 5, 5, 3, 1, 1, 4, 7, 14, 7, 4, 1, 1, 4, 12, 14, 14, 12, 4, 1, 1, 5, 12, 23, 42, 23, 12, 5, 1, 1, 5, 15, 30, 42, 42, 30, 15, 5, 1, 1, 6, 22, 55, 66, 132, 66, 55, 22, 6, 1, 1, 6, 22, 55, 99, 132, 132, 99, 55, 22, 6, 1, 1, 7, 26, 76, 143, 227, 429, 227, 143, 76, 26, 7, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 LINKS Alois P. Heinz, Antidiagonals n = 1..141, flattened Jean-Christophe Aval, François Bergeron, Interlaced rectangular parking functions, arXiv:1503.03991 [math.CO], 2015. FORMULA Some identities: A(n,k) = A(k,n); A(n,m*n) = A(n,m*n+1); A(n,n) = A000108(n); if n and k are coprime then A(n,k) = A071202(n,k). Sum_{k=1..n-1} A(n-k,k) = A298072(n)-2 for n>0. - Lee A. Newberg, Jan 18 2018 EXAMPLE Table starts: 1, 1, 1, 1, 1, 1, ... 1, 2, 2, 3, 3, 4, ... 1, 2, 5, 5, 7, 12, ... 1, 3, 5, 14, 14, 23, ... 1, 3, 7, 14, 42, 42, ... ... MAPLE b:= proc(x, y, r) option remember; `if`(y<0 or y>x*r, 0, `if`(x=0, 1, b(x-1, y, r) +b(x, y-1, r))) end: A:= (n, k)-> `if`(k x*r, 0, If[x == 0, 1, b[x - 1, y, r] + b[x, y - 1, r]]]; A[n_, k_] := If[k < n, b[k, n, n/k], b[n, k, k/n]]; Table[Table[A[n, 1 + d - n], {n, 1, d}], {d, 1, 14}] // Flatten (* Jean-François Alcover, Jan 30 2016, after Alois P. Heinz *) CROSSREFS Cf. A260419, A298072. Sequence in context: A090806 A241926 A174446 * A318045 A240656 A106476 Adjacent sequences: A071198 A071199 A071200 * A071202 A071203 A071204 KEYWORD nonn,tabl AUTHOR Henry Bottomley, May 16 2002 STATUS approved

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Last modified April 20 10:19 EDT 2024. Contains 371814 sequences. (Running on oeis4.)