OFFSET
1,1
COMMENTS
The forgotten topological index of a simple connected graph is the sum of the cubes of its vertex degrees.
REFERENCES
M. Imran and S. Hayat, On computation of topological indices of Aztec diamonds, Sci. Int. (Lahore), 26 (4), 1407-1412, 2014.
H. S. Ramanes and R. B. Jummannaver, Computation of Zagreb indices and forgotten index of Aztec diamond, Aryabhatta J. Math. and Informatics, Vol. 09, No. 01, 619-627, 2017.
LINKS
B. Furtula and I. Gutman, A forgotten topological index, J. Math. Chem. 53 (4), 1184-1190, 2015.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = 128*n^2 + 160*n - 84.
G.f.: 4*x*(51+34*x-21*x^2)/(1-x)^3. - Vincenzo Librandi, Sep 24 2017
EXAMPLE
a(1) = 204; indeed, the Aztec diamond AZ(1) has four vertices of degree 2, four vertices of degree 3, and one vertex of degree 4 (see p. 620 of the Ramanes et al. reference); consequently, a(1) = 4*8 + 4*27 + 1*64 = 32 + 108 + 64 = 204.
MAPLE
a := proc (n) options operator, arrow: 128*n^2+160*n-84 end proc: seq(a(n), n = 1 .. 40);
MATHEMATICA
Table[128 n^2 + 160 n - 84, {n, 36}] (* Michael De Vlieger, Sep 23 2017 *)
CoefficientList[Series[4 (51 + 34 x - 21 x^2) / (1-x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Sep 24 2017 *)
PROG
(Magma) [128*n^2+160*n-84: n in [1..40]]; // Vincenzo Librandi, Sep 24 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Sep 23 2017
STATUS
approved