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 A241628 Number of compositions of n with exactly three descents. 3
 3, 18, 78, 264, 786, 2097, 5179, 11998, 26400, 55593, 112814, 221639, 423318, 788518, 1436302, 2564135, 4494967, 7750068, 13160903, 22039386, 36434095, 59514365, 96139570, 153699716, 243345157, 381779187, 593848668, 916277405, 1403004758, 2132797015 (list; graph; refs; listen; history; text; internal format)
 OFFSET 9,1 LINKS Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 9..1000 EXAMPLE a(9) = 3: [2,1,3,2,1], [3,2,1,2,1], [2,1,2,1,2,1]. MAPLE b:= proc(n, i) option remember; `if`(n=0, 1, convert(series(add(b(n-j, j)* `if`(j coeff(b(n, 0), x, 3): seq(a(n), n=9..50); MATHEMATICA k = 3; 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[9, 50] (* Jean-François Alcover, Aug 27 2021, after Maple code *) CROSSREFS Column k=3 of A238343 and of A238344. Sequence in context: A094033 A245580 A043008 * A056319 A056310 A309259 Adjacent sequences: A241625 A241626 A241627 * A241629 A241630 A241631 KEYWORD nonn AUTHOR Joerg Arndt and Alois P. Heinz, Apr 26 2014 STATUS approved

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Last modified December 6 12:11 EST 2022. Contains 358634 sequences. (Running on oeis4.)