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Search: id:A152132
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| A152132 |
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Maximal length of rook tour on an n X n+1 board. |
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+0
9
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| 2, 8, 24, 54, 104, 174, 270, 396, 558, 756, 996, 1282, 1620, 2010, 2458, 2968, 3546, 4192, 4912, 5710, 6592, 7558, 8614, 9764, 11014, 12364, 13820, 15386, 17068, 18866, 20786, 22832, 25010, 27320, 29768, 32358, 35096, 37982, 41022, 44220, 47582
(list; graph; listen)
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OFFSET
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1,1
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REFERENCES
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M. Gardner, Knotted Doughnuts and Other Mathematical Entertainments. Freeman, NY, 1986, p. 76.
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FORMULA
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G.f.: -2*x*(-1-x-2*x^3-2*x^4-3*x^2+x^5)/(1+x)/(x^2+1)/(x-1)^4.
a(n)= 3*a(n-1) -3*a(n-2) +a(n-3) +a(n-4) -3*a(n-5) +3*a(n-6) -a(n-7). a(n) = 2*n^3/3+n^2-7*n/6+3/4-(-1)^n/4-A087960(n)/2. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 22 2009]
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MAPLE
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# Figure 43 of the Gardner book:
C := proc(n, m)
if type(m, even) and type(n, even) then
2 ;
elif type(m, odd) and type(n, odd) then
1 ;
elif type(m, even) and type(n, odd) and type(floor(n/2), even) then
3/2 ;
elif type(m, even) and type(n, odd) and type(floor(n/2), odd) then
1/2 ;
elif type(m, odd) and type(n, even) and type(floor(n/2), even) then
0 ;
elif type(m, odd) and type(n, even) and type(floor(n/2), odd) then
1 ;
fi;
end:
# formula for n X m boards, from the Gardner book:
T := proc(n, m)
n*(3*m^2+n^2-10)/6+C(n, m) ;
end:
for n from 1 to 24 do
m := n+3 ; # third diagonal here, for example
printf("%d, ", T(n, m)) ;
od:
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CROSSREFS
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Cf. A006071, A152133-A152135.
Sequence in context: A062247 A084744 A122547 this_sequence A009059 A009297 A083553
Adjacent sequences: A152129 A152130 A152131 this_sequence A152133 A152134 A152135
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KEYWORD
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nonn,easy
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AUTHOR
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R. J. Mathar, Mar 22 2009
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 22 2009
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