A366815 Hyper-Wiener index in diamond nanowires obtained by connecting n unit cells in a sequence.

448, 3544, 14294, 40420, 92348, 183208, 328834, 547764, 861240, 1293208, 1870318, 2621924, 3580084, 4779560, 6257818, 8055028, 10214064, 12780504, 15802630, 19331428, 23420588, 28126504, 33508274, 39627700, 46549288, 54340248, 63070494, 72812644

Offset

1,1

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Benedek Nagy, The hyper-Wiener Index of diamond nanowires, International Journal of Quantum Chemistry, e27258, 2024.

Wikipedia, Hyper-Wiener index.

Wikipedia, Diamond cubic.

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

Formula

a(n) = (338*n^4 + 481*n^3 + 145*n^2 + 416*n - 36)/3.

G.f.: 2*x*(224 + 652*x + 527*x^2 - 45*x^3 - 6*x^4)/(1 - x)^5. - Stefano Spezia, Oct 24 2023

Mathematica

LinearRecurrence[{5, -10, 10, -5, 1}, {448, 3544, 14294, 40420, 92348}, 50] (* Paolo Xausa, Feb 27 2024 *)

Prog

(PARI) a(n) = (338*n^4 + 481*n^3 + 145*n^2 + 416*n - 36)/3
(Magma) [(338*n^4 + 481*n^3 + 145*n^2 + 416*n - 36)/3 : n in [1..50]]; // Wesley Ivan Hurt, Dec 10 2023

Crossrefs

Cf. A366816.

Sequence in context: A348344 A234438 A048632 * A234428 A234424 A234175

Adjacent sequences: A366812 A366813 A366814 * A366816 A366817 A366818

Keyword

nonn,easy

Author

Benedek Nagy, Oct 24 2023

Status

approved