A292346 The forgotten topological index of the Aztec diamond AZ(n) (see the Ramanes et al. reference, Theorem 2.1).

204, 748, 1548, 2604, 3916, 5484, 7308, 9388, 11724, 14316, 17164, 20268, 23628, 27244, 31116, 35244, 39628, 44268, 49164, 54316, 59724, 65388, 71308, 77484, 83916, 90604, 97548, 104748, 112204, 119916, 127884, 136108, 144588, 153324, 162316, 171564

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

Table of n, a(n) for n=1..36.

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

Cf. A292343, A292344, A292345.

Sequence in context: A245468 A154518 A249285 * A338153 A234796 A234789

Adjacent sequences: A292343 A292344 A292345 * A292347 A292348 A292349

Keyword

nonn,easy

Author

Emeric Deutsch, Sep 23 2017

Status

approved