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 A186310 Total Wiener index of star-like trees with n edges. 0
 1, 4, 19, 54, 145, 350, 726, 1462, 2710, 4846, 8166, 13730, 21741, 34350, 52488, 79518, 117141, 172224, 246993, 353464, 496721, 694952, 958374, 1318174, 1789077, 2420888, 3243045, 4329098, 5728140, 7557906, 9893327, 12913820, 16746136 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS In the reference, p. 18, theorem 2.14, there is the following formula of the average Wiener index av(n) of a star-like tree with n edges: av(n) = 2*n^2 - (6^(1/2)*n^(3/2))/(2*Pi)*(log(n) + 2*cEuler - log(Pi^2/6) + 24*zeta(3)/(Pi^2)), so an approximate value of a(n) is given by av(n)*A058984(n). The following table was determined approximating zeta(3) by 1.2020569, and Euler's constant by 0.5772156649.     n  av(n)*A058984(n) (I)     a(n) (II)     I/II     5             136.9              145   0.94414    13           21443.1            21741   0.98630    20          352132.8           353464   0.99623    28         4329081.3          4329098   0.999996    29         5729910.2          5728140   1.00031    30         7560843.8          7557906   1.00039    33        16760543.2         16746136   1.00086    50       810144542.2        808929430   1.00150    60      5614575632.9       5606027232   1.00152    80    167110984160.2     166870656888   1.00144   100   3203299185861.4    3199052703248   1.00133   120  45208751880788.8   45153537110230   1.00122   130 155331813239050.0  155149438632558   1.00117   140 507674790104504.3  507101038817616   1.00113 For n<=28 the approximation underestimates the actual value of the total Wiener index of star-like trees. For 29 <= n <= 140 it overestimates this total; however as n grows, the rate I/II converges to 1. - Washington Bomfim, Feb 17 2011 REFERENCES S. Wagner, Graph-theoretical enumeration and digital expansions: an analytic approach, Dissertation, Fakult. f. Tech. Math. u. Tech. Physik, Tech. Univ. Graz, Austria, Feb. 2006. LINKS Washington Bomfim, Example Washington Bomfim, Table of n, a(n) for n=1..140 Arnold Knopfmacher, Robert F. Tichy, Stephan Wagner, and Volker Ziegler, Graphs, Partitions and Fibonacci Numbers EXAMPLE The first Bomfim link shows a way to find a(7). CROSSREFS Cf. A001620, A002117, A058984, A122681. Sequence in context: A159833 A166808 A253008 * A122684 A122681 A215862 Adjacent sequences:  A186307 A186308 A186309 * A186311 A186312 A186313 KEYWORD nonn AUTHOR Washington Bomfim, Feb 17 2011 STATUS approved

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Last modified May 21 09:30 EDT 2022. Contains 353908 sequences. (Running on oeis4.)