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A241627
Number of compositions of n with exactly two descents.
4
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
KEYWORD
nonn
AUTHOR
Joerg Arndt and Alois P. Heinz, Apr 26 2014
STATUS
approved