A302351 Hyper-Wiener index of body-centered cubic grid cells in a row.

92, 377, 1128, 2700, 5548, 10227, 17392, 27798, 42300, 61853, 87512, 120432, 161868, 213175, 275808, 351322, 441372, 547713, 672200, 816788, 983532, 1174587, 1392208, 1638750, 1916668, 2228517, 2576952, 2964728, 3394700, 3869823, 4393152, 4967842, 5597148

Offset: 1

Author

Benedek Nagy, Jun 09 2018

Keywords

• nonn
• easy

Links

• Colin Barker (Corrected by Harvey P. Dale), Table of n, a(n) for n = 1..1000
• Hamzeh Mujahed, Benedek Nagy, Hyper-Wiener Index on Rows of Unit Cells of the BCC Grid, Comptes rendus de l’Académie bulgare des Sciences, Tome 71, No 5, 2018, 675-684.
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Programs

Mathematica

Table[(25n^4+105n^3+143n^2+171n+108)/6,{n,40}] (* or *) LinearRecurrence[ {5,-10,10,-5,1},{92,377,1128,2700,5548},40] (* Harvey P. Dale, Sep 19 2020 *)

PARI

Vec(x*(92 - 83*x + 163*x^2 - 90*x^3 + 18*x^4 + 50*x^5 - 250*x^6 + 500*x^7 - 500*x^8 + 250*x^9 - 50*x^10) / (1 - x)^5 + O(x^40)) \\ Colin Barker, Jun 11 2018

Formula

a(n) = (25*n^4 + 105*n^3 + 143*n^2 + 171*n + 108)/6 (proven).

From Colin Barker, Jun 11 2018: (Start)

G.f.: x*(92 - 83*x + 163*x^2 - 90*x^3 + 18*x^4 + 50*x^5 - 250*x^6 + 500*x^7 - 500*x^8 + 250*x^9 - 50*x^10) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>11.

(End)

Extensions

Corrected and extended by Harvey P. Dale, Sep 19 2020