A241627 Number of compositions of n with exactly two descents.

2, 8, 29, 81, 205, 469, 1013, 2059, 4021, 7558, 13780, 24440, 42358, 71867, 119715, 196084, 316362, 503410, 791043, 1228636, 1888003, 2872541, 4330299, 6471778, 9594556, 14116745, 20622825, 29925512, 43149302, 61843197, 88130983, 124912824, 176132457

Offset

6,1

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 6..1000

Example

a(6) = 2: [3,2,1], [2,1,2,1].
a(7) = 8: [4,2,1], [3,2,1,1], [3,1,2,1], [1,3,2,1], [2,1,3,1], [1,2,1,2,1], [2,1,1,2,1], [2,1,2,1,1].

Maple

b:= proc(n, i) option remember;
      `if`(n=0, 1, convert(series(add(b(n-j, j)*
      `if`(j<i, x, 1), j=1..n), x, 3), polynom))
    end:
a:= n-> coeff(b(n, 0), x, 2):
seq(a(n), n=6..50);

Mathematica

k = 2;
b[n_, i_] := b[n, i] =  If[n == 0, 1, Sum[b[n - j, j]*
     If[j < i, x, 1], {j, n}] + O[x]^(k+1)];
a[n_] := SeriesCoefficient[b[n, 0], {x, 0, k}];
a /@ Range[6, 50] (* Jean-François Alcover, Aug 27 2021, after Maple code *)

Crossrefs

Column k=2 of A238343 and of A238344.

Sequence in context: A216785 A261559 A061230 * A293169 A306847 A364523

Adjacent sequences: A241624 A241625 A241626 * A241628 A241629 A241630

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Apr 26 2014

Status

approved