A307549
Number of longest paths in the n-Apollonian network.
Original entry on oeis.org
12, 174, 3084, 35971776, 2752830231727104, 9068533325994694179911466663936, 55357290942669201825421134704769198540735968154850291354435584
Offset: 1
A302718
Number of cycles in the n-Apollonian network.
Original entry on oeis.org
7, 119, 27850, 2635637428, 40538274896917926642, 18915440603912727411772352213199539580794, 4811072124719412065599148626063536230790419188877913496386013668865001860521888965
Offset: 1
-
P(c,d)={[2*d^3 + 7*d^2 + (6*c + 2)*d + 2*c, 3*d^2 + 5*d + (c + 1)]}
R(c,d)={16*d^3 + (9*c + 51)*d^2 + (30*c + 27)*d + (3*c^2 + 9*c + 4)}
a(n)={my(s=1, c=0, d=0); for(i=1, n, s = 3*s + R(c,d); [c,d]=P(c,d)); s} \\ Andrew Howroyd, Sep 10 2019
A301650
Number of longest cycles in the n-Apollonian network.
Original entry on oeis.org
3, 12, 162, 354294, 1694577218886, 38766491335360039793593446, 20288351481136358057581328834353447021191164711091366
Offset: 1
-
P(c,d,x)={[d^2 + 6*c*d + 2*d^3 + 2*x*(c + 3*d^2) + 2*x^2*d, c + d + 3*d^2 + 4*x*d + x^2]}
R(c,d,x)={4*d^3 + 9*c*d^2 + 3*d^2 + 6*c*d + 3*c^2 + 6*x*(2*d^3 + 3*d^2 + 4*c*d) + 3*x^2*(10*d^2 + 3*d + 3*c) + x^3*(18*d + 1) + 3*x^4}
a(n)={my(s=x^3, c=0, d=0); for(i=1, n, s = 3*s + R(c,d,x); [c,d]=P(c,d,x)); pollead(s)} \\ Andrew Howroyd, Sep 10 2019
Showing 1-3 of 3 results.
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