The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A180863 Wiener index of the n-sun graph. 2
 6, 21, 44, 75, 114, 161, 216, 279, 350, 429, 516, 611, 714, 825, 944, 1071, 1206, 1349, 1500, 1659, 1826, 2001, 2184, 2375, 2574, 2781, 2996, 3219, 3450, 3689, 3936, 4191, 4454, 4725, 5004, 5291, 5586, 5889, 6200, 6519, 6846, 7181, 7524, 7875, 8234, 8601 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS The Wiener index of a connected graph is the sum of distances between all unordered pairs of vertices in the graph. The Wiener polynomial of the n-sun graph is (1/2)*nt[(n-3)t^2+2(n-1)t+n+3]. Comment from Zachary Dove, Apr 19 2021 (Start) (Cf. A343560) On a square lattice, place the nonnegative integers at lattice points forming a spiral as follows: place "0" at the origin; then move one step downward (i.e., in the negative y direction) and place "1" at the lattice point reached; then turn 90 degrees in either direction and place a "2" at the next lattice point; then make another 90-degree turn in the same direction and place a "3" at the lattice point; etc. The terms of the sequence will lie parallel to the positive x-axis, located within the first quadrant, as seen in the example below: . 99 64--65--66--67--68--69--70--71--72 | | | 98 63 36--37--38--39--40--41--42 73 | | | | | 97 62 35 16--17--18--19--20 43 74 | | | | | | | 96 61 34 15 4---5--*6**21**44**75* | | | | | | | | | 95 60 33 14 3 0 7 22 45 76 | | | | | | | | | | 94 59 32 13 2---1 8 23 46 77 | | | | | | | | 93 58 31 12--11--10---9 24 47 78 | | | | | | 92 57 30--29--28--27--26--25 48 79 | | | | 91 56--55--54--53--52--51--50--49 80 | | 90--89--88--87--86--85--84--83--82--81 (End) LINKS Table of n, a(n) for n=2..47. B. E. Sagan, Y-N. Yeh and P. Zhang, The Wiener Polynomial of a Graph, Internat. J. of Quantum Chem., 60 (1996), 959-969. Eric Weisstein's World of Mathematics, Sun Graph. Eric Weisstein's World of Mathematics, Wiener Index. Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = n*(4*n-5). G.f.: x^2*(-6-3*x+x^2)/(x-1)^3. - Colin Barker, Oct 31 2012, adapted to new offset Sep 29 2021 a(n) = 3*a(n-1) - 3*a(n-2) + a(n). - Eric W. Weisstein, Sep 07 2017 a(n) = A033954(n-1)-1 = A033951(n-1) -1. -R. J. Mathar, Sep 29 2021 Sum_{n>=2} 1/a(n) = 1/5 - Pi/10 + 3*log(2)/5. - Amiram Eldar, Apr 16 2022 E.g.f.: exp(x)*(-x + 4*x^2) + x. - Nikolaos Pantelidis, Feb 10 2023 MAPLE seq(n*(4*n-5), n = 2 .. 50); MATHEMATICA (* Start from Eric W. Weisstein, Sep 07 2017, adapted to new offset *) Table[n (4 n - 5), {n, 2, 20}] LinearRecurrence[{3, -3, 1}, {6, 21, 44}, 20] CoefficientList[Series[(-6 - 3 x + x^2)/(-1 + x)^3, {x, 0, 20}], x] (* End *) PROG (PARI) a(n)=n*(4*n-5) \\ Charles R Greathouse IV, Jun 17 2017 CROSSREFS Sequence in context: A048036 A272671 A272684 * A180857 A119868 A175729 Adjacent sequences: A180860 A180861 A180862 * A180864 A180865 A180866 KEYWORD nonn,easy AUTHOR Emeric Deutsch, Sep 28 2010 EXTENSIONS a(2)=6 prefixed by R. J. Mathar, Sep 29 2021 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 31 17:17 EDT 2023. Contains 363068 sequences. (Running on oeis4.)