Search: id:A034828
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%I A034828
%S A034828 0,0,1,3,8,15,27,42,64,90,125,165,216,273,343,420,512,612,729,855,1000,
%T A034828 1155,1331,1518,1728,1950,2197,2457,2744,3045,3375,3720,4096,4488,4913,
%U A034828 5355,5832,6327,6859,7410,8000,8610,9261,9933,10648,11385,12167,12972,
               13824
%N A034828 a(n) = [n^2/4]*n/2.
%C A034828 Wiener index of cycle of length n.
%C A034828 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
%D A034828 H. J. Wiener, "Structural Determination of Paraffin Boiling Points." 
               J. Amer. Chem. Soc. 69, 17-20, 1947.
%D A034828 J. Zerovnik, Szeged index of symmetric graphs, J. Chem. Inf. Comput. 
               Sci., 39 (1999), 77-80.
%H A034828 T. D. Noe, <a href="b034828.txt">Table of n, a(n) for n=0..1000</a>
%H A034828 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               WienerIndex.html">Wiener Index</a>
%F A034828 a(n) = if n mod 2 = 1 then (n^2-1)*n/8 otherwise n^3/8.
%F A034828 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]
%F A034828 a(n) = (2*n^2 - 1 + (-1)^n) * n / 16. - Michael Somos Sep 06 2008
%F A034828 Euler transform of length 3 sequence [ 3, 2, -1]. - Michael Somos Sep 
               06 2008
%F A034828 a(-n) = -a(n). - Michael Somos Sep 06 2008
%e A034828 x^2 + 3*x^3 + 8*x^4 + 15*x^5 + 27*x^6 + 42*x^7 + 64*x^8 + 90*x^9 + ...
%o A034828 (PARI) {a(n) = (n^2 \ 4) * n / 2} /* Michael Somos Sep 06 2008 */
%o A034828 (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 
               */
%Y A034828 Equals A005996/2.
%Y A034828 Partial sums of A001318.
%Y A034828 Cf. A107231.
%Y A034828 A000578(n) = a(2*n). 3 * A000330(n) = a(2*n + 1). (n/2) * A002620(n) 
               = a(n). - Michael Somos Sep 06 2008
%Y A034828 Sequence in context: A047866 A080183 A109900 this_sequence A081276 A047837 
               A047873
%Y A034828 Adjacent sequences: A034825 A034826 A034827 this_sequence A034829 A034830 
               A034831
%K A034828 nonn,easy,nice
%O A034828 0,4
%A A034828 N. J. A. Sloane (njas(AT)research.att.com).
%E A034828 Definition reworded by Michael Somos Sep 06 2008

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