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 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

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