login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A302256 Hyper-Wiener index of rows of unit cells on the face-centered cubic lattice. 1
213, 942, 2956, 7326, 15447, 29038, 50142, 81126, 124681, 183822, 261888, 362542, 489771, 647886, 841522, 1075638, 1355517, 1686766, 2075316, 2527422, 3049663, 3648942, 4332486, 5107846, 5982897, 6965838, 8065192, 9289806, 10648851, 12151822 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This sequence is related to the Wiener-index of the FCC grid (cf. A273322). Now the second order distances are also counted (see definition of Hyper-Wiener index).

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

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" Constanta - Seria Matematica 26/1 (2018), 169-187.

Wikipedia, Hyper-Wiener index

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

FORMULA

a(n) = (81*n^4+261*n^3+264*n^2+540*n+132)/6. Proved in the Hamzeh Mujahed - Benedek Nagy paper.

a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5); with a(1)=213, a(2)=942, a(3)=2956, a(4)=7326 and a(5)=15447.

G.f.: x*(213 - 123*x + 376*x^2 - 164*x^3 + 22*x^4) / (1 - x)^5. - Colin Barker, Jun 11 2018

PROG

(PARI) a(n) = (81*n^4+261*n^3+264*n^2+540*n+132)/6; \\ Altug Alkan, Apr 04 2018

(PARI) Vec(x*(213 - 123*x + 376*x^2 - 164*x^3 + 22*x^4) / (1 - x)^5 + O(x^40)) \\ Colin Barker, Jun 11 2018

CROSSREFS

Cf. A273322.

Sequence in context: A251146 A085309 A252024 * A092127 A082967 A212312

Adjacent sequences:  A302253 A302254 A302255 * A302257 A302258 A302259

KEYWORD

nonn,easy

AUTHOR

Benedek Nagy, Apr 04 2018

EXTENSIONS

a(5) corrected by Altug Alkan, Apr 04 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 23 12:19 EDT 2021. Contains 346259 sequences. (Running on oeis4.)