A384844 Triangle read by rows: T(n,k) is the number of unordered pairs of nodes at distance k in the n-Dorogovtsev-Goltsev-Mendes graph.
3, 9, 6, 27, 57, 21, 81, 351, 369, 60, 243, 1806, 3582, 1716, 156, 729, 8472, 26346, 24216, 6648, 384, 2187, 37683, 165375, 241032, 128880, 22896, 912, 6561, 162177, 938907, 1946676, 1670280, 584784, 72624, 2112, 19683, 683112, 4979928, 13697148, 16889340, 9580368, 2366256, 216768, 4800
Offset: 1
Examples
Triangle begins:
3;
9, 6;
27, 57, 21;
81, 351, 369, 60;
243, 1806, 3582, 1716, 156;
729, 8472, 26346, 24216, 6648, 384;
2187, 37683, 165375, 241032, 128880, 22896, 912;
...
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..1275 (rows 1..50)
- Eric Weisstein's World of Mathematics, Dorogovtsev-Goltsev-Mendes Graph.
Programs
-
PARI
T(n)={ my(c=x^2*y/((1 - x)*(1 - 3*x + 2*(1 - y)*x^2)) + O(x*x^n), b=(1-2*x)*c/x, g = y*(1+b+2*c) + serconvol(b + c, b + c + y*c) + serconvol(y*c, b + 2*c)); [Vecrev(p/y)|p<-Vec(3*g/(1 - 3*x))]} { foreach(T(10), row, print(row)) } -
PARI
T(n)={my(g=3*(1 - 2*(3 + y)*x + 3*(3 - y + y^2)*x^2 - 4*(1 - y)^2*x^3)/((1 - x)*(1 - 3*x)*(1 - (5 + 4*y)*x + 4*(1 - y)^2*x^2))); [Vecrev(p)|p<-Vec(g + O(x^n))]} { foreach(T(10), row, print(row)) }
Formula
G.f.: 3*x*y*(1 - 2*(3 + y)*x + 3*(3 - y + y^2)*x^2 - 4*(1 - y)^2*x^3)/((1 - x)*(1 - 3*x)*(1 - (5 + 4*y)*x + 4*(1 - y)^2*x^2)).
A384843(n) = Sum_{k=1..n} k*T(n,k).