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

1,1

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).

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

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 *)

Prog

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

Crossrefs

Sequence in context: A030028 A320338 A250135 * A091077 A245991 A186637

Adjacent sequences: A273318 A273319 A273320 * A273322 A273323 A273324

Keyword

nonn,easy

Author

Benedek Nagy, May 20 2016

Status

approved