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A002714
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Number of different keys with 7 cuts, depths between 1 and 7 and tolerance 2 between adjacent cut depths.
(Formerly M4366 N1832)
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2
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7, 19, 53, 149, 421, 1193, 3387, 9627, 27383, 77923, 221805, 631469, 1797957, 5119593, 14578387, 41514003, 118218823, 336653331, 958698053, 2730124261, 7774706437, 22140438345, 63050541515, 179552587883, 511322221559
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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REFERENCES
| C. A. Coulson, How many keys?, Math. Gaz., 53 (1969), 7-13.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| C. A. Coulson, How Many different Keys?, Math. Gaz. vol 53 no 383 (1969), 7-13.
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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MAPLE
| A002714:=-(7-9*z-9*z**2+3*z**3)/(-1+4*z-2*z**2-4*z**3+z**4); [Conjectured by S. Plouffe in his 1992 dissertation. It appears to be correct.]
T := proc(d, n) option remember ; if n = 1 then 1; else if d = 7 then T(d, n-1)+T(d-1, n-1) ; elif d = 1 then T(d, n-1)+T(d+1, n-1) ; else T(d-1, n-1)+T(d, n-1)+T(d+1, n-1) ; fi ; fi ; end: A002714 := proc(n) local d ; add( T(d, n), d=1..7) ; end: seq(A002714(n), n=1..35) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 15 2008
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CROSSREFS
| Sequence in context: A092053 A072630 * A126361 A069005 A000413 A155335
Adjacent sequences: A002711 A002712 A002713 * A002715 A002716 A002717
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 15 2008
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