OFFSET
1,1
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, 2017.
LINKS
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = (4/3)*n*(12*n^3 + 44*n^2 + 36*n - 11).
G.f.: 4*x*(27 + 87*x - 23*x^2 + 5*x^3)/(1 - x)^5. - Vincenzo Librandi, Sep 24 2017
EXAMPLE
a(1) = 108; indeed, the Aztec diamond AZ(1) has 12 edges and 9 vertices (see p. 1409 of the Imran et al. reference); for each edge uv, none of the 9 vertices is equidistant from u and v; consequently, a(1) = 12*9 = 108.
MAPLE
a := proc (n) options operator, arrow: (4/3)*n*(12*n^3+44*n^2+36*n-11) end proc: seq(a(n), n = 1 .. 40);
MATHEMATICA
Table[(4/3) n (12 n^3 + 44 n^2 + 36 n - 11), {n, 31}] (* Michael De Vlieger, Sep 23 2017 *)
CoefficientList[Series[4 (27 + 87 x - 23 x^2 + 5 x^3) / (1 - x)^5, {x, 0, 40}], x] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {108, 888, 3268, 8560, 18460}, 40] (* Vincenzo Librandi, Sep 24 2017 *)
PROG
(Magma) [(4/3)*n*(12*n^3+44*n^2+36*n-11): n in [1..40]]; // Vincenzo Librandi, Sep 24 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Sep 23 2017
STATUS
approved