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Search: id:A143461
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| A143461 |
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Square array A(n,k) of numbers of length n quaternary words with at least k 0-digits between any other digits (n,k >= 0), read by antidiagonals. |
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+0
8
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| 1, 1, 4, 1, 4, 16, 1, 4, 7, 64, 1, 4, 7, 19, 256, 1, 4, 7, 10, 40, 1024, 1, 4, 7, 10, 22, 97, 4096, 1, 4, 7, 10, 13, 43, 217, 16384, 1, 4, 7, 10, 13, 25, 73, 508, 65536, 1, 4, 7, 10, 13, 16, 46, 139, 1159, 262144, 1, 4, 7, 10, 13, 16, 28, 76, 268, 2683, 1048576, 1, 4, 7, 10
(list; table; graph; listen)
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OFFSET
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0,3
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FORMULA
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G.f. of column k: 1/(x^k*(1-x-3*x^(k+1))). A(n,k) = 4^n if k=0, else A(n,k) = 3*n+1 if n<=k+1, else A(n,k) = A(n-1,k) + 3*A(n-k-1,k).
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EXAMPLE
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A (3,1) = 19, because 19 quaternary words of length 3 have at least 1 0-digit between any other digits: 000, 001, 002, 003, 010, 020, 030, 100, 101, 102, 103, 200, 201, 202, 203, 300, 301, 301, 303.
Square array A(n,k) begins:
1 1 1 1 1 1 1 1 ...
4 4 4 4 4 4 4 4 ...
16 7 7 7 7 7 7 7 ...
64 19 10 10 10 10 10 10 ...
256 40 22 13 13 13 13 13 ...
1024 97 43 25 16 16 16 16 ...
4096 217 73 46 28 19 19 19 ...
16384 508 139 76 49 31 22 22 ...
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MAPLE
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A := proc (n::nonnegint, k::nonnegint) option remember; if k=0 then 4^n elif n<=k+1 then 3*n+1 else A(n-1, k) +3*A(n-k-1, k) fi end: seq (seq (A(n, d-n), n=0..d), d=0..13);
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CROSSREFS
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Column k=0: A000302, k=1: A006130(n+1), k=2: A084386(n+2), k=3: A143454, k=4: A143455, k=5: A143456, k=6: A143457, k=7: A143458, k=8: A143459, k=9: A143460. Diagonal: A016777.
Sequence in context: A165487 A055886 A132478 this_sequence A066808 A033918 A136467
Adjacent sequences: A143458 A143459 A143460 this_sequence A143462 A143463 A143464
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KEYWORD
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nonn,tabl
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AUTHOR
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Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 16 2008
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