id:A031878 - OEIS Search Results

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Maximal number of edges in Hamiltonian path in complete graph on n nodes.

+0
3

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; listen)

	OFFSET	`1,3`
	FORMULA	`C(n, 2) if n odd, C(n, 2)-n/2+1 if n even; G.f.: x^2(1+2x+x^3)/((1-x)(1-x^2)).` `a(n)= ( nn +n -(n-1)*(n mod 2) )/2, (frank.ellermann(AT)t-online.de).`
	EXAMPLE	`E.g. for n=4 [1:2][2:3][3:1][1:4][4:2], so a(4) = 5.`
	CROSSREFS	`Cf. A031940.` `Sequence in context: A034746 A080931 A165718 this_sequence A160792 A137395 A001767` `Adjacent sequences: A031875 A031876 A031877 this_sequence A031879 A031880 A031881`
	KEYWORD	`nonn`
	AUTHOR	`Colin L. Mallows (colinm(AT)research.avayalabs.com)`

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.

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