OFFSET
1,1
COMMENTS
The n-web graph is the stacked prism graph C_n X P_3 with the edges of the outer cycle removed.
Equivalently, the n-web graph is obtained by attaching a pendant edge to each node of the outer cycle of the circular ladder (prism) C_n X P_2.
The Wiener index of a connected graph is the sum of distances between all unordered pairs of vertices in the graph.
a(n) = sum(A180575(n,k), k>=1).
Sequence extended to a(1)-a(2) using the formula/recurrence. - Eric W. Weisstein, Sep 08 2017
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.
Eric Weisstein's World of Mathematics, Web Graph
Eric Weisstein's World of Mathematics, Wiener Index
Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).
FORMULA
a(2n) = n*(9*n^2+20*n-2); a(2n+1) = (2*n+1)*(9*n^2+29*n+8)/2.
G.f.: -x^3*(27*x^5-50*x^4-35*x^3+110*x^2-10*x-69)/((x-1)^4*(x+1)^2). - Colin Barker, Oct 31 2012
a(n) = n*(2*n*(9*n+40)+9*(-1)^n-25)/16. - Bruno Berselli, Oct 31 2012
MAPLE
a := proc (n) if `mod`(n, 2) = 1 then (1/8)*n*(9*n^2+40*n-17) else (1/8)*n*(9*n^2+40*n-8) end if end proc: seq(a(n), n = 3 .. 45);
MATHEMATICA
Table[n (-25 + 9 (-1)^n + 2 n (40 + 9 n))/16, {n, 20}] (* Eric W. Weisstein, Sep 08 2017 *)
LinearRecurrence[{2, 1, -4, 1, 2, -1}, {4, 27, 69, 148, 255, 4178}, 20] (* Eric W. Weisstein, Sep 08 2017 *)
CoefficientList[Series[(4 + 19 x + 11 x^2 - x^3 - 6 x^4 + 3761 x^5)/((-1 + x)^4 (1 + x)^2), {x, 0, 20}], x] (* Eric W. Weisstein, Sep 08 2017 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Sep 19 2010
EXTENSIONS
a(1)-a(2) from Eric W. Weisstein, Sep 08 2017
STATUS
approved