A083196 a(n) = 8*n^4 + 9*n^2 + 2.

2, 19, 166, 731, 2194, 5227, 10694, 19651, 33346, 53219, 80902, 118219, 167186, 230011, 309094, 407027, 526594, 670771, 842726, 1045819, 1283602, 1559819, 1878406, 2243491, 2659394, 3130627, 3661894, 4258091, 4924306, 5665819, 6488102, 7396819, 8397826

Offset

0,1

Comments

Minimal norm of a sequence of 3-D lattices that converges to the FCC lattice.

Links

Table of n, a(n) for n=0..32.

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

Formula

From Elmo R. Oliveira, May 25 2026: (Start)

G.f.: (2 + 9*x + 91*x^2 + 71*x^3 + 19*x^4)/(1 - x)^5.

E.g.f.: (2 + 17*x + 65*x^2 + 48*x^3 + 8*x^4)*exp(x).

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). (End)

Mathematica

Table[8n^4+9n^2+2, {n, 0, 40}] (* Harvey P. Dale, Nov 26 2018 *)

Prog

(PARI) a(n)=8*n^4+9*n^2+2 \\ Charles R Greathouse IV, Oct 21 2022

Crossrefs

Cf. A082942.

Sequence in context: A057858 A065898 A290188 * A037526 A037735 A224753

Adjacent sequences: A083193 A083194 A083195 * A083197 A083198 A083199

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 17 2008

Status

approved