A273322 Wiener index of graphs of f.c.c. unit cells in a line = Sum of distances in face-centered cubic grid unit cells connected in a row.

150, 536, 1336, 2712, 4826, 7840, 11916, 17216, 23902, 32136, 42080, 53896, 67746, 83792, 102196, 123120, 146726, 173176, 202632, 235256, 271210, 310656, 353756, 400672, 451566, 506600, 565936, 629736, 698162, 771376, 849540, 932816, 1021366

Offset: 1

Author

Benedek Nagy, May 20 2016

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Hamzeh Mujahed, Benedek Nagy, Wiener index on rows of unit cells of the face-centred cubic lattice, Acta Crystallographica, Section A: Foundations and Advances, Volume A72, Part 2 (2016), 243-249.
• Hamzeh Mujahed, Benedek Nagy, Exact Formula for Computing the Hyper-Wiener Index on Rows of Unit Cells of the Face-Centred Cubic Lattice, Analele Universitatii Ovidius Constanţa-Seria Matematica Vol. 26(1), 2018, 169-187.
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Programs

Mathematica

Table[27 n^3 + 45 n^2 + 62 n + 16, {n, 33}] (* or *)
Rest@ CoefficientList[Series[2 x (75 - 32 x + 46 x^2 - 8 x^3)/(1 - x)^4, {x, 0, 33}], x] (* Michael De Vlieger, May 20 2016 *)
LinearRecurrence[{4,-6,4,-1},{150,536,1336,2712},40] (* Harvey P. Dale, Dec 04 2018 *)

PARI

Vec(2*x*(75-32*x+46*x^2-8*x^3)/(1-x)^4 + O(x^50)) \\ Colin Barker, May 20 2016

Formula

a(n) = 27*n^3 + 45*n^2 + 62*n + 16.

From Colin Barker, May 20 2016: (Start)

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 4.

G.f.: 2*x*(75 - 32*x + 46*x^2 - 8*x^3) / (1-x)^4.

(End)