A273321 Wiener index of graph of b.c.c. unit cells in a line = Sum of distances in a b.c.c. row graph.

64, 206, 488, 960, 1672, 2674, 4016, 5748, 7920, 10582, 13784, 17576, 22008, 27130, 32992, 39644, 47136, 55518, 64840, 75152, 86504, 98946, 112528, 127300, 143312, 160614, 179256, 199288, 220760, 243722, 268224, 294316, 322048, 351470, 382632, 415584, 450376, 487058, 525680, 566292

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 Lines of Unit Cells of the Body-Centered Cubic Grid, Mathematical Morphology and Its Applications to Signal and Image Processing, Volume 9082 of the series Lecture Notes in Computer Science, pp. 597-606.
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Programs

Mathematica

Table[(25/3) n^3 + 20 n^2 + (71/3) n + 12, {n, 40}] (* or *)
Rest@ CoefficientList[Series[2 x (32 - 25 x + 24 x^2 - 6 x^3)/(1 - x)^4, {x, 0, 40}], x] (* Michael De Vlieger, May 20 2016 *)

PARI

Vec(2*x*(32-25*x+24*x^2-6*x^3)/(1-x)^4 + O(x^50)) \\ Colin Barker, May 20 2016

Formula

a(n) = (25/3)*n^3 + 20*n^2 + (71/3)*n + 12.

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.

O.g.f.: 2*x*(32 - 25*x + 24*x^2 - 6*x^3) / (1 - x)^4. (End)

E.g.f.: (12 + 52*x + 45*x^2 + (25/3)*x^3)*exp(x) - 12. - Benedict W. J. Irwin, May 27 2016