OFFSET
1,1
COMMENTS
Row n has k in the range 1..1+floor(2*n/3).
Table gives the coefficients of the Wiener polynomials. The degree of the polynomial corresponds to the diameter of the graph.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..883
Eric Weisstein's World of Mathematics, Apollonian Network
Eric Weisstein's World of Mathematics, Wiener Index
EXAMPLE
Triangle begins:
6;
15, 6;
42, 72, 6;
123, 522, 258;
366, 2970, 3894, 396;
1095, 14838, 37332, 13680, 216;
3282, 68736, 278490, 224928, 24624;
9843, 303918, 1779678, 2517228, 754704, 22032;
29526, 1303938, 10269150, 22233096, 13114656, 1489104, 7776;
...
MATHEMATICA
R[dp_, peq_, p1_, p2_] := {3*(dp - x + peq^2 + (2 + 7*x)*p1^2 + (7 + 2*x)*p2^2 + (4 + 2*x)*peq*p1 + 6*peq*p2 + 2*(4 + 5*x)*p1*p2 + x*(peq + 3*p1 + 3*p2)), x*(1 + 3*p1), 2*(p1 + p2), peq + p2};
A[n_] := (v = {6*x, x, 0, 0}; For[i = 2, i <= n, i++, v = R @@ v]; v[[1]]);
Table[CoefficientList[A[n], x] // Rest, {n, 1, 10}] // Flatten (* Jean-François Alcover, Dec 28 2017, after Andrew Howroyd *)
PROG
(PARI)
R(dp, peq, p1, p2, x) = {[3*(dp - x + peq^2 + (2+7*x)*p1^2 + (7+2*x)*p2^2 + (4+2*x)*peq*p1 + 6*peq*p2 + 2*(4+5*x)*p1*p2 + x*(peq+3*p1+3*p2)), x*(1+3*p1), 2*(p1+p2), peq+p2]}
A(n, x) = {my(v=[6*x, x, 0, 0, x]); for(i=2, n, v=R(v[1], v[2], v[3], v[4], x)); v[1]}
for (n=1, 10, print(Vec(polrecip(A(n, x))), "; " ))
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Andrew Howroyd, Sep 02 2017
STATUS
approved