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A180574
Wiener index of the n-sunlet graph.
3
27, 60, 105, 174, 259, 376, 513, 690, 891, 1140, 1417, 1750, 2115, 2544, 3009, 3546, 4123, 4780, 5481, 6270, 7107, 8040, 9025, 10114, 11259, 12516, 13833, 15270, 16771, 18400, 20097, 21930, 23835, 25884, 28009, 30286, 32643, 35160, 37761, 40530
OFFSET
3,1
LINKS
B. E. Sagan, Y-N. Yeh and P. Zhang, The Wiener Polynomial of a Graph, Internat. J. of Quantum Chem., 60, 1996, 959-969.
D. Stevanovic, Hosoya polynomial of composite graphs, Discrete Math., 235 (2001), 237-244.
Eric Weisstein's World of Mathematics, Sunlet Graph
Eric Weisstein's World of Mathematics, Wiener Index
Y.-N. Yeh and I. Gutman, On the sum of all distances in composite graphs, Discrete Math., 135 (1994), 359-365.
FORMULA
a(n) = Sum(A180573(n,k),k>=1).
a(n) = n(n^2+4n-2)/2 if n is even; a(n) = n(n^2+4n-3)/2 if n is odd.
a(n) = n*(-5+(-1)^n+8*n+2*n^2)/4. - Colin Barker, Oct 31 2012
G.f.: -x^3*(5*x^2-2*x-9)*(2*x^3-3*x^2+3)/((x-1)^4*(x+1)^2). - Colin Barker, Oct 31 2012
a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6). - Eric W. Weisstein, Sep 07 2017
MAPLE
a := proc (n) if `mod`(n, 2) = 0 then (1/2)*n*(n^2+4*n-2) else (1/2)*n*(n^2+4*n-3) end if end proc: seq(a(n), n = 3 .. 45);
MATHEMATICA
Table[n (-5 + (-1)^n + 2 n (4 + n))/4, {n, 3, 20}]
LinearRecurrence[{2, 1, -4, 1, 2, -1}, {27, 60, 105, 174, 259, 376}, 20]
CoefficientList[Series[(27 + 6 x - 42 x^2 + 12 x^3 + 19 x^4 - 10 x^5)/((-1 + x)^4 (1 + x)^2), {x, 0, 20}], x]
CROSSREFS
Cf. A180573.
Sequence in context: A039459 A235164 A157500 * A107580 A138610 A128530
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Sep 19 2010
STATUS
approved