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
KEYWORD
nonn,easy
AUTHOR
Benedek Nagy, Oct 24 2023
STATUS
approved