A356768 - OEIS

%I #30 Jun 10 2024 00:17:56

%S 0,6,168,1404,6720,23250,65016,156408,336384,663390,1221000,2124276,

%T 3526848,5628714,8684760,13014000,19009536,27149238,38007144,52265580,

%U 70728000,94332546,124166328,161480424,207705600,264468750,333610056,417200868,517562304

%N a(n) = (n^2+n+1)*(n^2+n)*n^2.

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

%H Kaplan, Nathan; Kimport, Susie; Lawrence, Rachel; Peilen, Luke; Weinreich, Max <a href="https://doi.org/10.1007/s00022-017-0391-1">Counting arcs in projective planes via Glynn’s algorithm</a>, J. Geom. 108, No. 3, 1013-1029 (2017), Th. 1.4 C_3.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).

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

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

%F 6 | a(n).

%t 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 *)

%o (Python)

%o def A356768(n): return n**3*(n*(n*(n + 2) + 2) + 1) # _Chai Wah Wu_, Aug 29 2022

%Y Cf. A169938 (2-arcs).

%K nonn,easy

%O 0,2

%A _R. J. Mathar_, Aug 29 2022