A366817 Detour index of n body-centered cubic grid unit cells in a row.
64, 298, 752, 1476, 2520, 3934, 5768, 8072, 10896, 14290, 18304, 22988, 28392, 34566, 41560, 49424, 58208, 67962, 78736, 90580, 103544, 117678, 133032, 149656, 167600, 186914, 207648, 229852, 253576, 278870, 305784, 334368, 364672, 396746, 430640
Offset: 1
Links
- Paolo Xausa, Table of n, a(n) for n = 1..10000
- Benedek Nagy and H. Mujahed, Detour index for body-centred cubic grid with unit cells connected in a row, Comptes Rendus de l'Académie Bulgare des Sciences, 74(11), 1581-1589 (2021).
- Eric Weisstein's World of Mathematics, Detour Index
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Programs
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Mathematica
A366817[n_] := (25*n^3 + 180*n^2 - 13*n)/3; Array[A366817, 50] (* or *) LinearRecurrence[{4, -6, 4, -1}, {64, 298, 752, 1476}, 50] (* Paolo Xausa, May 28 2024 *)
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PARI
a(n) = (25*n^3 + 180*n^2 - 13*n)/3 \\ Andrew Howroyd, Oct 24 2023
Formula
a(n) = (25*n^3 + 180*n^2 - 13*n)/3.
From Stefano Spezia, May 28 2024: (Start)
G.f.: 2*x*(32 + 21*x - 28*x^2)/(1 - x)^4.
E.g.f.: exp(x)*x*(192 + 255*x + 25*x^2)/3. (End)