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Search: id:A034828
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| 0, 0, 1, 3, 8, 15, 27, 42, 64, 90, 125, 165, 216, 273, 343, 420, 512, 612, 729, 855, 1000, 1155, 1331, 1518, 1728, 1950, 2197, 2457, 2744, 3045, 3375, 3720, 4096, 4488, 4913, 5355, 5832, 6327, 6859, 7410, 8000, 8610, 9261, 9933, 10648, 11385, 12167, 12972, 13824
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Wiener index of cycle of length n.
The Weisstein link and the H. J. Wiener reference expand on the previous comment: "Wiener index of cycle of length n." - Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 04 2008
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REFERENCES
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H. J. Wiener, "Structural Determination of Paraffin Boiling Points." J. Amer. Chem. Soc. 69, 17-20, 1947.
J. Zerovnik, Szeged index of symmetric graphs, J. Chem. Inf. Comput. Sci., 39 (1999), 77-80.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
Eric Weisstein's World of Mathematics, Wiener Index
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FORMULA
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a(n) = if n mod 2 = 1 then (n^2-1)*n/8 otherwise n^3/8.
G.f.: x^2*(1+x+x^2)/((1-x)^2*(1-x^2)^2); a(n)=2a(n-1)+a(n-2)-4a(n-3)+a(n-4)+2a(n-5)-a(n-6); a(n)=(2n^3+12n^2+23n+14)/16+(n+2)(-1)^n/16; a(n)=sum{k=0..floor((n+2)/2), ((n+2)/(n+2-k))(-1)^k*C(n+2-k, k)C(n-2k+2, 2)C(n-2k, floor((n-2k)/2))}. - Paul Barry (pbarry(AT)wit.ie), May 13 2005 [Typo corrected by R. J. Mathar, Aug 18 2008]
a(n) = (2*n^2 - 1 + (-1)^n) * n / 16. - Michael Somos Sep 06 2008
Euler transform of length 3 sequence [ 3, 2, -1]. - Michael Somos Sep 06 2008
a(-n) = -a(n). - Michael Somos Sep 06 2008
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EXAMPLE
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x^2 + 3*x^3 + 8*x^4 + 15*x^5 + 27*x^6 + 42*x^7 + 64*x^8 + 90*x^9 + ...
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PROGRAM
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(PARI) {a(n) = (n^2 \ 4) * n / 2} /* Michael Somos Sep 06 2008 */
(PARI) {a(n) = if( n<0, -a(-n), polcoeff( x^2 * (1 + x + x^2) / ((1 - x)^2 * (1 - x^2)^2) + x * O(x^n), n))} /* Michael Somos Sep 06 2008 */
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CROSSREFS
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Equals A005996/2.
Partial sums of A001318.
Cf. A107231.
A000578(n) = a(2*n). 3 * A000330(n) = a(2*n + 1). (n/2) * A002620(n) = a(n). - Michael Somos Sep 06 2008
Adjacent sequences: A034825 A034826 A034827 this_sequence A034829 A034830 A034831
Sequence in context: A047866 A080183 A109900 this_sequence A081276 A047837 A047873
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KEYWORD
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nonn,easy,nice
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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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Definition reworded by Michael Somos Sep 06 2008
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