A356768 a(n) = (n^2+n+1)*(n^2+n)*n^2.

0, 6, 168, 1404, 6720, 23250, 65016, 156408, 336384, 663390, 1221000, 2124276, 3526848, 5628714, 8684760, 13014000, 19009536, 27149238, 38007144, 52265580, 70728000, 94332546, 124166328, 161480424, 207705600, 264468750, 333610056, 417200868, 517562304

Offset

0,2

Comments

Numer of ordered 3-arcs in the projective plane of order 3.

Links

Table of n, a(n) for n=0..28.

Kaplan, Nathan; Kimport, Susie; Lawrence, Rachel; Peilen, Luke; Weinreich, Max Counting arcs in projective planes via Glynn’s algorithm, J. Geom. 108, No. 3, 1013-1029 (2017), Th. 1.4 C_3.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

a(n) = n^2*A169938(n).

G.f.: -6*x*(1+21*x+59*x^2+35*x^3+4*x^4)/(x-1)^7.

6 | a(n).

Mathematica

Table[(n^2+n+1)(n^2+n)n^2, {n, 0, 30}] (* or *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 6, 168, 1404, 6720, 23250, 65016}, 30] (* Harvey P. Dale, Dec 25 2023 *)

Prog

(Python)
def A356768(n): return n**3*(n*(n*(n + 2) + 2) + 1) # Chai Wah Wu, Aug 29 2022

Crossrefs

Cf. A169938 (2-arcs).

Sequence in context: A143534 A104729 A106661 * A322708 A181013 A003720

Adjacent sequences: A356765 A356766 A356767 * A356769 A356770 A356771

Keyword

nonn,easy

Author

R. J. Mathar, Aug 29 2022

Status

approved