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A128094
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Number of sequences s of length n, with s[1]=1, s[2]=1, s[3]=1, s[k-1] <=s[k] <= s[k-1]+s[k-2]+s[k-3] (s is called a sub-tribonacci sequence of length n).
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1
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1, 3, 9, 36, 228, 2196, 33901, 862503, 36346723, 2564238411, 304902857694, 61384367733677, 21020435566780278, 12292402317454051941, 12319906894146608845054, 21234027294331775378957366
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OFFSET
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3,2
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LINKS
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FORMULA
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See the Maple program; f[k](x,y,z) is the number of sequences s[1], s[2], ..., s[k+3] such that s[1]=x, s[2]=y, s[3]=z, s[j-1] <=s[j] <= s[j-3]+s[j-2]+s[j-1].
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EXAMPLE
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a(5)=9 because we have (1,1,1,1,1), (1,1,1,1,2), (1,1,1,1,3), (1,1,1,2,2), (1,1,1,2,3), (1,1,1,2,4), (1,1,1,3,3), (1,1,1,3,4), (1,1,1,3,5).
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MAPLE
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f[0]:=1:for k from 0 to 20 do f[k+1]:=factor(sum(subs({x=y, y=z, z=u}, f[k]), u=z..x+y+z)) od: seq(subs({x=1, y=1, z=1}, f[k]), k=0..20);
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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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