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A307212
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a(n) is the Narumi-Katayama index of the Lucas cube Lambda(n).
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2
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0, 2, 3, 256, 38880, 1289945088, 42855402240000000, 605828739547255327948800000000, 13263549731442762279026688000000000000000000000000000, 1334793240853871268746431553848403294648071618560000000000000000000000000000000000000000000
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OFFSET
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1,2
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COMMENTS
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The Lucas cube Lambda(n) can be defined as the graph whose vertices are the binary strings of length n without either two consecutive 1's or a 1 in the first and in the last position, and in which two vertices are adjacent when their Hamming distance is exactly 1.
The Narumi-Katayama index of a connected graph is the product of the degrees of the vertices of the graph.
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LINKS
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EXAMPLE
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a(2) = 2 because the Lucas cube Lambda(2) is the path-tree P_3 having 2 vertices of degree 1 and 1 vertex of degree 2; consequently, the Narumi-Katayama index is 1*1*2 = 2.
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MAPLE
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G := (1+(1-y)*x+x^2*y^2+(1-y)*x^3*y-(1-y)^2*x^4*y)/((1-x*y)*(1-x^2*y)-x^3*y):
g := expand(series(G, x=0, 40)): T := (n, k) -> coeff(coeff(g, x, n), y, k):
a := n -> mul(k^T(n, k), k=0..n): lprint(seq(a(n), n=1..10));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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