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A289722
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Irregular triangle read by rows: T(n,k) is the number of unordered pairs of nodes at distance k in the n-Apollonian network.
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5
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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;
...
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MATHEMATICA
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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]]);
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PROG
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(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))), "; " ))
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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