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A294281
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Number of ascent sequences of length n with alternating ascents and descents (unaffected by level steps).
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2
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1, 1, 2, 4, 9, 22, 59, 172, 547, 1886, 7047, 28360, 122675, 567210, 2796999, 14641044, 81191947, 475148678, 2929442263, 18965690560, 128754649699, 914056305794, 6777666961735, 52367331911180, 421188392986843, 3519168714308702, 30519733808467031
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = Sum_{j=0..n} binomial(n-1,j) * A099960(n-j).
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EXAMPLE
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a(3) = 4: 000, 001, 010, 011.
a(4) = 9: 0000, 0001, 0010, 0011, 0100, 0101, 0102, 0110, 0111.
a(5) = 22: 00000, 00001, 00010, 00011, 00100, 00101, 00102, 00110, 00111, 01000, 01001, 01002, 01010, 01011, 01020, 01021, 01022, 01100, 01101, 01102, 01110, 01111.
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MAPLE
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b:= proc(n, i, t, u) option remember; `if`(n<1, 1, add(
b(n-1, j, t+`if`(j>i, 1, 0), `if`(i=j, u, 1-u)),
j=`if`(u=0, i..t+1, 0..i)))
end:
a:= n-> b(n-1, 0$3):
seq(a(n), n=0..30);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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