A180574 Wiener index of the n-sunlet graph.

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

Author

Emeric Deutsch, Sep 19 2010

Keywords

• nonn
• easy

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.
• Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).

Crossrefs

Cf. A180573.

Programs

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]

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