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A031878
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Maximal number of edges in Hamiltonian path in complete graph on n nodes.
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2
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0, 1, 3, 5, 10, 13, 21, 25, 36, 41, 55, 61, 78, 85, 105, 113, 136, 145, 171, 181, 210, 221, 253, 265, 300, 313, 351, 365, 406, 421, 465, 481, 528, 545, 595, 613, 666, 685, 741, 761, 820, 841, 903, 925, 990, 1013, 1081, 1105, 1176, 1201, 1275, 1301, 1378
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Quasipolynomial of order 2. [Charles R Greathouse IV, Dec 07 2011]
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (1,2,-2,-1,1).
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FORMULA
| C(n, 2) if n odd, C(n, 2)-n/2+1 if n even; G.f.: x^2*(1+2*x+x^3)/((1-x)*(1-x^2)).
a(n)= ( n*n +n -(n-1)*(n mod 2) )/2. [Frank Ellermann (hmdmhdfmhdjmzdtjmzdtzktdkztdjz(AT)gmail.com)]
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EXAMPLE
| E.g. for n=4 [1:2][2:3][3:1][1:4][4:2], so a(4) = 5.
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PROG
| (PARI) a(n)=if(n%2, n^2-n, n^2-2*n+2)/2 \\ Charles R Greathouse IV, Dec 07 2011
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CROSSREFS
| Cf. A031940.
Sequence in context: A080931 A200919 A165718 * A160792 A137395 A001767
Adjacent sequences: A031875 A031876 A031877 * A031879 A031880 A031881
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KEYWORD
| nonn,easy
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AUTHOR
| Colin L. Mallows (colinm(AT)research.avayalabs.com)
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