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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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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; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 0..10010
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FORMULA
| 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
| 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
| A:= proc (n, k) 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
| Columns k=0-9: A000302, A006130(n+1), A084386(n+2), A143454, A143455, A143456, A143457, A143458, A143459, A143460. Diagonal: A016777.
Sequence in context: A055886 A132478 A205125 * A066808 A033918 A136467
Adjacent sequences: A143458 A143459 A143460 * A143462 A143463 A143464
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KEYWORD
| nonn,tabl
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AUTHOR
| Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 16 2008
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