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Search: id:A007723
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| A007723 |
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Triangle a(n,k) of number of M-sequences read by antidiagonals. |
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| 1, 1, 2, 1, 2, 2, 1, 2, 3, 2, 1, 2, 4, 4, 2, 1, 2, 5, 8, 5, 2, 1, 2, 6, 15, 16, 6, 2, 1, 2, 7, 26, 52, 32, 7, 2, 1, 2, 8, 42, 152, 203, 64, 8, 2, 1, 2, 9, 64, 392, 1144, 877, 128, 9, 2, 1, 2, 10, 93, 904, 5345, 10742, 4140, 256, 10, 2, 1, 2, 11, 130, 1899, 20926, 102050, 122772, 21147
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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S. Linusson, The number of M-sequences and f-vectors, Combinatorica, 19 (1999), 255-266.
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LINKS
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S. Linusson, The number of M-sequences and f-vectors, Combinatorica, 19 (1999), 255-266.
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FORMULA
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a(p, n)=sum_{-1<=k<=n} Lp(n, k) where Lp(n, k) satisfies the recurrence: Lp(n, k) = sum_{k<=i<=n} L(p-1, n, i)*L(p, i-1, k-1) for p, n>=1, k>=0 with the boundary conditions: Lp(n, n)=Lp(n, -1)=1 for all p>=1, n>=-1; L0(n, n)=L0(n, -1)=1 and L0(n, k)=0 for k different from -1 or n - Pab Ter (pabrlos2(AT)yahoo.com), Nov 10 2005
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MAPLE
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L:=proc(p, n, k) options remember: local i: if (k=-1 or k=n) and n>=-1 and p>=1 then RETURN(1) elif p=0 and (k=-1 or k=n) then RETURN(1) elif p=0 and (k<>-1 and k<>n) then RETURN(0) elif p>=1 and n>=1 then RETURN(add(L(p-1, n, i)*L(p, i-1, k-1), i=k..n)) fi: end; M:=(p, n)->add(L(p, n, k), k=-1..n); seq(seq(M(n-i+1, i-1), i=0..n+1), n=-1..12); # first method (Pab Ter)
L:=proc(p, n, k) options remember: local i: if (k=-1 or k=n) and n>=-1 and p>=1 then RETURN(1) elif p=0 and (k=-1 or k=n) then RETURN(1) elif p=0 and (k<>-1 and k<>n) then RETURN(0) elif p>=1 and n>=1 then RETURN(add(L(p-1, n, i)*L(p, i-1, k-1), i=k..n)) fi: end; M:=proc(p, n) options remember: local i: if n<1 and n>-2 and p>=0 then RETURN([1, 2][n+2]) elif p=0 and n>=0 then RETURN(2) elif p>=1 and n>=1 then RETURN(1+add(L(p-1, n, i)*M(p, i-1), i=0..n)) fi: end; seq(seq(M(n-i+1, i-1), i=0..n+1), n=-1..12); # 2nd method (Pab Ter)
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CROSSREFS
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Cf. A003659, A011819, A011820, etc., A007065, A007625.
Sequence in context: A140223 A014643 A118382 this_sequence A067437 A029315 A070080
Adjacent sequences: A007720 A007721 A007722 this_sequence A007724 A007725 A007726
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Pab Ter (pabrlos2(AT)yahoo.com), Nov 10 2005
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