A386851 a(n) = floor(5*n^2/6).

0, 3, 7, 13, 20, 30, 40, 53, 67, 83, 100, 120, 140, 163, 187, 213, 240, 270, 300, 333, 367, 403, 440, 480, 520, 563, 607, 653, 700, 750, 800, 853, 907, 963, 1020, 1080, 1140, 1203, 1267, 1333, 1400, 1470, 1540, 1613, 1687, 1763, 1840, 1920, 2000, 2083, 2167, 2253

Offset: 1

Author

Chai Wah Wu, Aug 05 2025

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (1,1,0,-1,-1,1).

Crossrefs

Cf. A227347 (partial sums), A330451.

Programs

Mathematica

a[n_]:=Floor[5n^2/6];Array[a,52] (* or *)  Rest[CoefficientList[Series[-x^2*(3*x^2 + 4*x + 3)/((x - 1)^3*(x + 1)*(x^2 + x + 1)),{x,0,52}],x]] (* or *) LinearRecurrence[{1,1,0,-1,-1,1},{0, 3, 7, 13, 20, 30, 40},52] (* James C. McMahon, Aug 12 2025 *)

Python

def A386851(n): return 5*n**2//6

Formula

a(n) = A227347(n)-A227347(n-1) for n>1.

a(n) = a(n-1) + a(n-2) - a(n-4) - a(n-5) + a(n-6) for n > 6.

a(2n) = A330451(n).

G.f.: -x^2*(3*x^2 + 4*x + 3)/((x - 1)^3*(x + 1)*(x^2 + x + 1)).