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Search: id:A143291
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| A143291 |
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Triangle T(n,k), n>=2, 0<=k<=n-2, read by rows, of numbers of binary words of length n containing at least one subword 10^{k}1 and no subwords 10^{i}1 with i<k. |
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+0
14
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| 1, 3, 1, 8, 2, 1, 19, 4, 2, 1, 43, 8, 3, 2, 1, 94, 15, 5, 3, 2, 1, 201, 27, 9, 4, 3, 2, 1, 423, 48, 15, 6, 4, 3, 2, 1, 880, 84, 24, 10, 5, 4, 3, 2, 1, 1815, 145, 38, 16, 7, 5, 4, 3, 2, 1, 3719, 248, 60, 24, 11, 6, 5, 4, 3, 2, 1, 7582, 421, 94, 35, 17, 8, 6, 5, 4, 3, 2, 1, 15397, 710, 146
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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G.f. of column k: x^(k+2)/((x^(k+1)+x-1)(x^(k+2)+x-1)).
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EXAMPLE
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T (5,1) = 4, because there are 4 words of length 5 containing at least one subword 101 and no subword 11: 00101, 01010, 10100, 10101.
Triangle begins:
[1]
[3, 1]
[8, 2, 1]
[19, 4, 2, 1]
[43, 8, 3, 2, 1]
[94, 15, 5, 3, 2, 1]
[201, 27, 9, 4, 3, 2, 1]
[423, 48, 15, 6, 4, 3, 2, 1]
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MAPLE
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as := proc (n, k::nonnegint) option remember; if k=0 then 2^n elif n<=k and n>= 0 then n+1 elif n>0 then as(n-1, k) + as(n-k-1, k) else as(n+1+k, k) - as(n+k, k) fi end; T := proc (n, k::nonnegint) as(n, k) - as(n, k+1) end; seq (seq (T(n, k), k=0..n-2), n=2..15);
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CROSSREFS
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Cf. A008466 (column k=0), A143281 (column k=1) A143282 (column k=2) A143283 (column k=3) A143284 (column k=4) A143285 (column k=5) A143286 (column k=6) A143287 (column k=7) A143288 (column k=8) A143289 (column k=9) A143290 (column k=10).
Row sums are in A000295, A125128. [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jun 01 2009]
Sequence in context: A155789 A112420 A010288 this_sequence A077111 A073072 A049541
Adjacent sequences: A143288 A143289 A143290 this_sequence A143292 A143293 A143294
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 04 2008
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