A243237 Number of isoscent sequences of length n with maximal number of ascents.
1, 1, 1, 4, 3, 25, 17, 2, 172, 53, 7, 1422, 436, 72, 5, 7894, 1854, 271, 19, 86372, 19919, 3179, 312, 14, 527951, 102503, 14324, 1287, 56, 7237537, 1373018, 198783, 20572, 1350, 42, 48862041, 8055893, 1032239, 96532, 5866, 174, 801902467, 129068117, 16767855
Offset: 0
Keywords
Links
- Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 0..100
Programs
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Maple
b:= proc(n, i, t) option remember; `if`(n<1, 1, expand(add( `if`(j>i, x, 1) *b(n-1, j, t+`if`(j=i, 1, 0)), j=0..t+1))) end: a:= n-> (p-> coeff(p, x, degree(p)))(b(n-1, 0$2)): seq(a(n), n=0..50); -
Mathematica
b[n_, i_, t_] := b[n, i, t] = If[n < 1, 1, Expand[Sum[ If[j > i, x, 1]*b[n - 1, j, t + If[j == i, 1, 0]], {j, 0, t + 1}]]]; a[n_] := With[{p = b[n - 1, 0, 0]}, Coefficient[p, x, Exponent[p, x]]]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Aug 27 2021, after Maple code *)
Formula
a(n) = A242351(n,n+3-ceiling(2*sqrt(n+2))).