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A273321 Wiener index of graph of b.c.c. unit cells in a line = Sum of distances in a b.c.c. row graph. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 18 13:12 EDT 2019. Contains 326100 sequences. (Running on oeis4.)