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A120933
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Triangle read by rows: T(n,k) is the number of binary words of length n for which the length of the maximal leading nondecreasing subword is k (1<=k<=n).
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0
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2, 1, 3, 2, 2, 4, 4, 4, 3, 5, 8, 8, 6, 4, 6, 16, 16, 12, 8, 5, 7, 32, 32, 24, 16, 10, 6, 8, 64, 64, 48, 32, 20, 12, 7, 9, 128, 128, 96, 64, 40, 24, 14, 8, 10, 256, 256, 192, 128, 80, 48, 28, 16, 9, 11, 512, 512, 384, 256, 160, 96, 56, 32, 18, 10, 12, 1024, 1024, 768, 512, 320
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Row sums are the powers of 2 (A000079). Sum(k*T(n,k), k=1..n)=3*2^n-n-3=A095151(n).
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FORMULA
| T(n,k)=k*2^(n-k-1) if k<n; T(n,n)=n+1. G=G(t,z)=(1-2z+tz^2)/[(1-2z)(1-tz)^2] - 1.
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EXAMPLE
| T(4,2)=4 because we have 0100,0101,1100 and 1101.
Triangle starts:
2;
1,3;
2,2,4;
4,4,3,5;
8,8,6,4,6;
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MAPLE
| T:=proc(n, k) if k<n then k*2^(n-k-1) elif k=n then n+1 else 0 fi end: for n from 1 to 13 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form;
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CROSSREFS
| Cf. A000079, A095151.
Sequence in context: A144329 A141157 A137948 * A064134 A144154 A054710
Adjacent sequences: A120930 A120931 A120932 * A120934 A120935 A120936
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KEYWORD
| nonn,tabl
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 16 2006
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