A306823 a(n) is the second multiplicative Zagreb index of the Lucas cube Lambda(n).
1, 4, 27, 1048576, 45916502400000, 237376313799769806328950291431424, 18897697257047055734419223897702400000000000000000000000000000000000
Offset: 1
Keywords
Examples
a(2)=4 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, a(2) = 1^1*1^1*2^2 = 4. a(4)=1048576 because the Lucas cube Lambda(4) is a bouquet of tw 4-cycles, having 6 vertices of degree 2 and 1 vertex of degree 4; consequently, a(4) = (2^2)^6*4^4 = 2^12*v^4 = 1048576.
Links
- Alois P. Heinz, Table of n, a(n) for n = 1..11
- I. Gutman, Multiplicative Zagreb indices of trees, Bulletin of International Mathematical Virtual Institute ISSN 1840-4367, Vol. 1, 2011, 13-19.
- S. Klavžar, Structure of Fibonacci cubes: a survey, J. Comb. Optim., 25, 2013, 505-522.
- S. Klavžar, M. Mollard and M. Petkovšek, The degree sequence of Fibonacci and Lucas cubes, Discrete Mathematics, Vol. 311, No. 14 (2011), 1310-1322.
Programs
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Maple
G:=(1+(1-t)*z+t^2*z^2+t*(1-t)*z^3-t*(1-t)^2*z^4)/((1-t*z)*(1-t*z^2)-t*z^3): Gser:=simplify(series(G, z=0,50)): for n from 0 to 45 do P[n]:=sort(coeff(Gser,z,n)) od: seq(product(j^(j*coeff(P[n],t,j)),j=1..n), n=1..7);
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