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

Author

Benedek Nagy, Oct 24 2023

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A366816.

Programs

Magma

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

Mathematica

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

PARI

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

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